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Sample records for reaction-diffusion cellular automaton

  1. Glider-based computing in reaction-diffusion hexagonal cellular automata

    International Nuclear Information System (INIS)

    Adamatzky, Andrew; Wuensche, Andrew; De Lacy Costello, Benjamin

    2006-01-01

    A three-state hexagonal cellular automaton, discovered in [Wuensche A. Glider dynamics in 3-value hexagonal cellular automata: the beehive rule. Int J Unconvention Comput, in press], presents a conceptual discrete model of a reaction-diffusion system with inhibitor and activator reagents. The automaton model of reaction-diffusion exhibits mobile localized patterns (gliders) in its space-time dynamics. We show how to implement the basic computational operations with these mobile localizations, and thus demonstrate collision-based logical universality of the hexagonal reaction-diffusion cellular automaton

  2. Reaction-diffusion path planning in a hybrid chemical and cellular-automaton processor

    International Nuclear Information System (INIS)

    Adamatzky, Andrew; Lacy Costello, Benjamin de

    2003-01-01

    To find the shortest collision-free path in a room containing obstacles we designed a chemical processor and coupled it with a cellular-automaton processor. In the chemical processor obstacles are represented by sites of high concentration of potassium iodide and a planar substrate is saturated with palladium chloride. Potassium iodide diffuses into the substrate and reacts with palladium chloride. A dark coloured precipitate of palladium iodide is formed almost everywhere except sites where two or more diffusion wavefronts collide. The less coloured sites are situated at the furthest distance from obstacles. Thus, the chemical processor develops a repulsive field, generated by obstacles. A snapshot of the chemical processor is inputted to a cellular automaton. The automaton behaves like a discrete excitable media; also, every cell of the automaton is supplied with a pointer that shows an origin of the cell's excitation. The excitation spreads along the cells corresponding to precipitate depleted sites of the chemical processor. When the destination-site is excited, waves travel on the lattice and update the orientations of the pointers. Thus, the automaton constructs a spanning tree, made of pointers, that guides a traveler towards the destination point. Thus, the automaton medium generates an attractive field and combination of this attractive field with the repulsive field, generated by the chemical processor, provides us with a solution of the collision-free path problem

  3. Cellular automaton model of mass transport with chemical reactions

    International Nuclear Information System (INIS)

    Karapiperis, T.; Blankleider, B.

    1993-10-01

    The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes advection and diffusion in a simple way, and as no restriction is placed on the number of particles at a lattice site, it is also able to describe a wide variety of chemical reactions. Assuming molecular chaos and a smooth density function, we obtain the standard reaction-transport equations in the continuum limit. Simulations on one-and two-dimensional lattices show that the discrete model can be used to approximate the solutions of the continuum equations. We discuss discrepancies which arise from correlations between molecules and how these discrepancies disappear as the continuum limit is approached. Of particular interest are simulations displaying long-time behaviour which depends on long-wavelength statistical fluctuations not accounted for by the standard equations. The model is applied to the reactions a + b ↔ c and a + b → c with homogeneous and inhomogeneous initial conditions as well as to systems subject to autocatalytic reactions and displaying spontaneous formation of spatial concentration patterns. (author) 9 figs., 34 refs

  4. Cellular automaton model of coupled mass transport and chemical reactions

    International Nuclear Information System (INIS)

    Karapiperis, T.

    1994-01-01

    Mass transport, coupled with chemical reactions, is modelled as a cellular automaton in which solute molecules perform a random walk on a lattice and react according to a local probabilistic rule. Assuming molecular chaos and a smooth density function, we obtain the standard reaction-transport equations in the continuum limit. The model is applied to the reactions a + b ↔c and a + b →c, where we observe interesting macroscopic effects resulting from microscopic fluctuations and spatial correlations between molecules. We also simulate autocatalytic reaction schemes displaying spontaneous formation of spatial concentration patterns. Finally, we propose and discuss the limitations of a simple model for mineral-solute interaction. (author) 5 figs., 20 refs

  5. Multidimensional traveling waves in the Allen–Cahn cellular automaton

    International Nuclear Information System (INIS)

    Murata, Mikio

    2015-01-01

    Ultradiscretization is a limiting procedure transforming a given difference equation into a cellular automaton. The cellular automaton constructed by this procedure preserves the essential properties of the original equation, such as the structure of exact solutions for integrable equations. In this article, a cellular automaton analog of the multidimensional Allen–Cahn equation which is not an integrable system is constructed by the ultradiscretization. Moreover, the traveling wave solutions for the resulting cellular automaton are given. The shape, behavior and stability of the solutions in ultradiscrete systems are similar to those in continuous systems. (paper)

  6. Cellular automatons applied to gas dynamic problems

    Science.gov (United States)

    Long, Lyle N.; Coopersmith, Robert M.; Mclachlan, B. G.

    1987-01-01

    This paper compares the results of a relatively new computational fluid dynamics method, cellular automatons, with experimental data and analytical results. This technique has been shown to qualitatively predict fluidlike behavior; however, there have been few published comparisons with experiment or other theories. Comparisons are made for a one-dimensional supersonic piston problem, Stokes first problem, and the flow past a normal flat plate. These comparisons are used to assess the ability of the method to accurately model fluid dynamic behavior and to point out its limitations. Reasonable results were obtained for all three test cases, but the fundamental limitations of cellular automatons are numerous. It may be misleading, at this time, to say that cellular automatons are a computationally efficient technique. Other methods, based on continuum or kinetic theory, would also be very efficient if as little of the physics were included.

  7. An improved cellular automaton method to model multispecies biofilms.

    Science.gov (United States)

    Tang, Youneng; Valocchi, Albert J

    2013-10-01

    Biomass-spreading rules used in previous cellular automaton methods to simulate multispecies biofilm introduced extensive mixing between different biomass species or resulted in spatially discontinuous biomass concentration and distribution; this caused results based on the cellular automaton methods to deviate from experimental results and those from the more computationally intensive continuous method. To overcome the problems, we propose new biomass-spreading rules in this work: Excess biomass spreads by pushing a line of grid cells that are on the shortest path from the source grid cell to the destination grid cell, and the fractions of different biomass species in the grid cells on the path change due to the spreading. To evaluate the new rules, three two-dimensional simulation examples are used to compare the biomass distribution computed using the continuous method and three cellular automaton methods, one based on the new rules and the other two based on rules presented in two previous studies. The relationship between the biomass species is syntrophic in one example and competitive in the other two examples. Simulation results generated using the cellular automaton method based on the new rules agree much better with the continuous method than do results using the other two cellular automaton methods. The new biomass-spreading rules are no more complex to implement than the existing rules. Copyright © 2013 Elsevier Ltd. All rights reserved.

  8. The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton

    Directory of Open Access Journals (Sweden)

    Oleg Evsutin

    2016-08-01

    Full Text Available This article is devoted to the application of the cellular automata mathematical apparatus to the problem of continuous optimization. The cellular automaton with an objective function is introduced as a new modification of the classic cellular automaton. The algorithm of continuous optimization, which is based on dynamics of the cellular automaton having the property of geometric symmetry, is obtained. The results of the simulation experiments with the obtained algorithm on standard test functions are provided, and a comparison between the analogs is shown.

  9. Level Set Structure of an Integrable Cellular Automaton

    Directory of Open Access Journals (Sweden)

    Taichiro Takagi

    2010-03-01

    Full Text Available Based on a group theoretical setting a sort of discrete dynamical system is constructed and applied to a combinatorial dynamical system defined on the set of certain Bethe ansatz related objects known as the rigged configurations. This system is then used to study a one-dimensional periodic cellular automaton related to discrete Toda lattice. It is shown for the first time that the level set of this cellular automaton is decomposed into connected components and every such component is a torus.

  10. Cellular automaton-based position sensitive detector equalization

    Energy Technology Data Exchange (ETDEWEB)

    Ferrando, Nestor [Grupo de Diseno de Sistemas Digitales, Instituto de Aplicaciones de las Tecnologias de la Informacion y de las Comunicaciones Avanzadas, Universidad Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia (Spain)], E-mail: nesferjo@upvnet.upv.es; Herrero, V.; Cerda, J.; Lerche, C.W.; Colom, R.J.; Gadea, R.; Martinez, J.D.; Monzo, J.M.; Mateo, F.; Sebastia, A.; Benlloch, J.M. [Grupo de Diseno de Sistemas Digitales, Instituto de Aplicaciones de las Tecnologias de la Informacion y de las Comunicaciones Avanzadas, Universidad Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia (Spain)

    2009-06-01

    Indirect position detectors based on scintillator crystals lack of spacial uniformity in their response. This happens due to crystal inhomogeneities and gain differences among the photomultiplier anodes. In order to solve this, PESIC, an integrated front-end for multianode photomultiplier based nuclear imaging devices was created. One of its main features is the digitally programmable gain adjustment for every photomultiplier output. On another front, cellular automata have been proved to be a useful method for dynamic system modeling. In this paper, a cellular automaton which emulates the behavior of the scintillator crystal, the photomultiplier and the front-end is introduced. Thanks to this model, an automatic energy-based calibration of the detector can be done by configuring the cellular automaton with experimental data and making it evolve up to an stable state. This can be useful as a precalibration method of the detector.

  11. Cellular automaton-based position sensitive detector equalization

    International Nuclear Information System (INIS)

    Ferrando, Nestor; Herrero, V.; Cerda, J.; Lerche, C.W.; Colom, R.J.; Gadea, R.; Martinez, J.D.; Monzo, J.M.; Mateo, F.; Sebastia, A.; Benlloch, J.M.

    2009-01-01

    Indirect position detectors based on scintillator crystals lack of spacial uniformity in their response. This happens due to crystal inhomogeneities and gain differences among the photomultiplier anodes. In order to solve this, PESIC, an integrated front-end for multianode photomultiplier based nuclear imaging devices was created. One of its main features is the digitally programmable gain adjustment for every photomultiplier output. On another front, cellular automata have been proved to be a useful method for dynamic system modeling. In this paper, a cellular automaton which emulates the behavior of the scintillator crystal, the photomultiplier and the front-end is introduced. Thanks to this model, an automatic energy-based calibration of the detector can be done by configuring the cellular automaton with experimental data and making it evolve up to an stable state. This can be useful as a precalibration method of the detector.

  12. Simulation of diffusion in a two-dimensional lattice gas cellular automaton: a test of mode-coupling theory

    NARCIS (Netherlands)

    Frenkel, D.; Ernst, M.H.

    1989-01-01

    We compute the velocity autocorrelation function of a tagged particle in a two-dimensional lattice-gas cellular automaton using a method that is about a million times more efficient than existing techniques. A t-1 algebraic tail in the tagged-particle velocity autocorrelation function is clearly

  13. Soliton cellular automaton associated with Dn(1)-crystal B2,s

    Science.gov (United States)

    Misra, Kailash C.; Wilson, Evan A.

    2013-04-01

    A solvable vertex model in ferromagnetic regime gives rise to a soliton cellular automaton which is a discrete dynamical system in which site variables take on values in a finite set. We study the scattering of a class of soliton cellular automata associated with the U_q(D_n^{(1)})-perfect crystal B2, s. We calculate the combinatorial R matrix for all elements of B2, s ⊗ B2, 1. In particular, we show that the scattering rule for our soliton cellular automaton can be identified with the combinatorial R matrix for U_q(A_1^{(1)}) oplus U_q(D_{n-2}^{(1)})-crystals.

  14. Cellular automaton simulation of the diffusive motion of bacteria and their adhesion to nanostructures on a solid surface.

    Science.gov (United States)

    Yamamoto, Takehiro; Emura, Chie; Oya, Masashi

    2016-12-01

    The growth of a biofilm begins with the adhesion of bacteria to a solid surface. Consequently, biofilm growth can be managed by the control of bacterial adhesion. Recent experimental studies have suggested that bacterial adhesion can be controlled by modifying a solid surface using nanostructures. Computational prediction and analysis of bacterial adhesion behavior are expected to be useful for the design of effective arrangements of nanostructures for controlling bacterial adhesion. The present study developed a cellular automaton (CA) model for bacterial adhesion simulation that could describe both the diffusive motion of bacteria and dependence of their adhesion patterns on the distance between nanostructures observed in experimental studies. The diffusive motion was analyzed by the moment scaling spectrum theory, and the present model was confirmed to describe subdiffusion behavior due to obstacles. Adhesion patterns observed in experimental studies can be successfully simulated by introducing CA rules to describe a mechanism by which bacteria tend to move to increase the area of contact with nanostructures. Copyright © 2016 Elsevier Ltd. All rights reserved.

  15. Application of a novel cellular automaton porosity prediction model to aluminium castings

    International Nuclear Information System (INIS)

    Atwood, R.C.; Chirazi, A.; Lee, P.D.

    2002-01-01

    A multiscale model was developed to predict the formation of porosity within a solidifying aluminium-silicon alloy. The diffusion of silicon and dissolved gas was simulated on a microscopic scale combined with cellular automaton models of gas porosity formation within the growing three-dimensional solidification microstructure. However, due to high computational cost, the modelled volume is limited to the millimetre range. This renders the application of direct modelling of complex shape castings unfeasible. Combining the microstructural modelling with a statistical response-surface prediction method allows application of the microstructural model results to industrial scale casts by incorporating them in commercial solidification software. (author)

  16. An outline of cellular automaton universe via cosmological KdV equation

    Science.gov (United States)

    Christianto, V.; Smarandache, F.; Umniyati, Y.

    2018-03-01

    It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework. This paper can be considered as our second attempt towards such a complete description of the Universe based on soliton wave solution of cosmological KdV equation. Then we advance further this KdV equation by virtue of Cellular Automaton method to solve the PDEs. We submit wholeheartedly Robert Kuruczs hypothesis that Big Bang should be replaced with a finite cellular automaton universe with no expansion [4][5]. Nonetheless, we are fully aware that our model is far from being complete, but it appears the proposed cellular automaton model of the Universe is very close in spirit to what Konrad Zuse envisaged long time ago. It is our hope that the new proposed method can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details.

  17. Solutions of the lattice sine–Gordon equation and the solitons of its cellular automaton

    International Nuclear Information System (INIS)

    Willox, R; Ramani, A; Grammaticos, B

    2014-01-01

    We analyse the solutions of the cellular automaton sine–Gordon equation and link them to solutions of the discrete, lattice, sine–Gordon. We show that while the ultradiscretizable, positive definite, solutions of the latter behave dispersively, certain parts of these dispersive waves nonetheless survive in the ultradiscrete limit, giving rise to the solutions of the cellular automaton. We examine the ultradiscrete solutions in the case of a generalized cellular automaton in which the dependent variable can assume non-integer values and we show that the collision of two solitary waves is inelastic, leading to the creation of a ‘bridge’ of constant height that links two outgoing structures. Based on the ultradiscrete form of the sine–Gordon equation we explain the appearance of this bridging region and we describe its interaction with a solitary wave. (paper)

  18. Cellular automata for spatiotemporal pattern formation from reaction–diffusion partial differential equations

    International Nuclear Information System (INIS)

    Ohmori, Shousuke; Yamazaki, Yoshihiro

    2016-01-01

    Ultradiscrete equations are derived from a set of reaction–diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction–diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction–diffusion equations. (author)

  19. Mixing of two-component flow in a simplified stirred tank with cellular automaton method; Cellular automaton ho ni yoru kakuhan sonai no niseibunryu no kongo keisan

    Energy Technology Data Exchange (ETDEWEB)

    Watanabe, S; Takahashi, R [Tokyo Institute of Technology, Tokyo (Japan)

    1996-01-25

    The applicability of a cellular automaton technique to engineering problems will be examined by dealing with mixing in multicomponent flow. The quality and accumulation rate of the product depend on the mixing of raw materials basically. After thoroughly understanding the mixing process, we optimize the geometrical allocation of such elements as a propeller with casing, a chimney and a product output nozzle in a reactor. Usually mixing is formulated by partial differential equations of conservation laws and empirical formulae, and solved numerically by the finite difference technique. In order to evaluate the fine structure of time-dependent interfacial behavior in multicomponent flow, the cellular automaton technique is used, since this has an advantage of describing the pattern formation in detail. It will be demonstrated in the present paper that mixing of two-component immiscible flow is reasonably simulated mesoscopically. 13 refs., 17 figs.

  20. New cellular automaton designed to simulate geometration in gel electrophoresis

    Science.gov (United States)

    Krawczyk, M. J.; Kułakowski, K.; Maksymowicz, A. Z.

    2002-08-01

    We propose a new kind of cellular automaton to simulate transportation of molecules of DNA through agarose gel. Two processes are taken into account: reptation at strong electric field E, described in the particle model, and geometration, i.e. subsequent hookings and releases of long molecules at and from gel fibres. The automaton rules are deterministic and they are designed to describe both processes within one unified approach. Thermal fluctuations are not taken into account. The number of simultaneous hookings is limited by the molecule length. The features of the automaton are: (i) the size of the cell neighbourhood for the automaton rule varies dynamically, from nearest neighbors to the entire molecule; (ii) the length of the time step is determined at each step according to dynamic rules. Calculations are made up to N=244 reptons in a molecule. Two subsequent stages of the motion are found. Firstly, an initial set of random configurations of molecules is transformed into a more ordered phase, where most molecules are elongated along the applied field direction. After some transient time, the mobility μ reaches a constant value. Then, it varies with N as 1/ N for long molecules. The band dispersion varies with time t approximately as Nt1/2. Our results indicate that the well-known plateau of the mobility μ vs. N does not hold at large electric fields.

  1. The threshold of coexistence and critical behaviour of a predator-prey cellular automaton

    International Nuclear Information System (INIS)

    Arashiro, Everaldo; Tome, Tania

    2007-01-01

    We study a probabilistic cellular automaton to describe two population biology problems: the threshold of species coexistence in a predator-prey system and the spreading of an epidemic in a population. By carrying out mean-field approximations and numerical simulations we obtain the phase boundaries (thresholds) related to the transition between an active state, where prey and predators present a stable coexistence, and a prey absorbing state. The numerical estimates for the critical exponents show that the transition belongs to the directed percolation universality class. In the limit where the cellular automaton maps into a model for the spreading of an epidemic with immunization we observe a crossover from directed percolation class to the dynamic percolation class. Patterns of growing clusters related to species coexistence and spreading of epidemic are shown and discussed

  2. Emergent 1d Ising Behavior in AN Elementary Cellular Automaton Model

    Science.gov (United States)

    Kassebaum, Paul G.; Iannacchione, Germano S.

    The fundamental nature of an evolving one-dimensional (1D) Ising model is investigated with an elementary cellular automaton (CA) simulation. The emergent CA simulation employs an ensemble of cells in one spatial dimension, each cell capable of two microstates interacting with simple nearest-neighbor rules and incorporating an external field. The behavior of the CA model provides insight into the dynamics of coupled two-state systems not expressible by exact analytical solutions. For instance, state progression graphs show the causal dynamics of a system through time in relation to the system's entropy. Unique graphical analysis techniques are introduced through difference patterns, diffusion patterns, and state progression graphs of the 1D ensemble visualizing the evolution. All analyses are consistent with the known behavior of the 1D Ising system. The CA simulation and new pattern recognition techniques are scalable (in both dimension, complexity, and size) and have many potential applications such as complex design of materials, control of agent systems, and evolutionary mechanism design.

  3. Pseudo-random number generation using a 3-state cellular automaton

    Science.gov (United States)

    Bhattacharjee, Kamalika; Paul, Dipanjyoti; Das, Sukanta

    This paper investigates the potentiality of pseudo-random number generation of a 3-neighborhood 3-state cellular automaton (CA) under periodic boundary condition. Theoretical and empirical tests are performed on the numbers, generated by the CA, to observe the quality of it as pseudo-random number generator (PRNG). We analyze the strength and weakness of the proposed PRNG and conclude that the selected CA is a good random number generator.

  4. Global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms

    International Nuclear Information System (INIS)

    Wang Jian; Lu Junguo

    2008-01-01

    In this paper, we study the global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain a sufficient condition for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy cellular neural networks with delays and reaction-diffusion terms. The result imposes constraint conditions on the network parameters independently of the delay parameter. The result is also easy to check and plays an important role in the design and application of globally exponentially stable fuzzy neural circuits

  5. Stability analysis of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms

    International Nuclear Information System (INIS)

    Li Zuoan; Li Kelin

    2009-01-01

    In this paper, we investigate a class of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. By employing the delay differential inequality with impulsive initial conditions and M-matrix theory, we find some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. In particular, the estimate of the exponential converging index is also provided, which depends on the system parameters. An example is given to show the effectiveness of the results obtained here.

  6. Cellular automaton modeling of biological pattern formation characterization, examples, and analysis

    CERN Document Server

    Deutsch, Andreas

    2017-01-01

    This text explores the use of cellular automata in modeling pattern formation in biological systems. It describes several mathematical modeling approaches utilizing cellular automata that can be used to study the dynamics of interacting cell systems both in simulation and in practice. New in this edition are chapters covering cell migration, tissue development, and cancer dynamics, as well as updated references and new research topic suggestions that reflect the rapid development of the field. The book begins with an introduction to pattern-forming principles in biology and the various mathematical modeling techniques that can be used to analyze them. Cellular automaton models are then discussed in detail for different types of cellular processes and interactions, including random movement, cell migration, adhesive cell interaction, alignment and cellular swarming, growth processes, pigment cell pattern formation, tissue development, tumor growth and invasion, and Turing-type patterns and excitable media. In ...

  7. Cellular automaton for surface reactions

    Energy Technology Data Exchange (ETDEWEB)

    Pechatnikov, E L [AN SSSR, Chernogolovka (Russian Federation). Otdelenie Inst. Khimicheskoj Fiziki; Frankowicz, A; Danielak, R [Uniwersytet Jagiellonski, Cracow (Poland)

    1994-06-01

    A new algorithm which overcomes some specific difficulties arising in modeling of heterogeneous catalytic processes by cellular automata (CA) technique is proposed. The algorithm was tested with scheme introduced by Ziff, Gulari and Barshad and showed a good agreement with their results. The problem of the physical adequacy and interpretation of the algorithm was discussed. (author). 10 refs, 4 figs.

  8. Cellular automaton decoders of topological quantum memories in the fault tolerant setting

    International Nuclear Information System (INIS)

    Herold, Michael; Eisert, Jens; Kastoryano, Michael J; Campbell, Earl T

    2017-01-01

    Active error decoding and correction of topological quantum codes—in particular the toric code—remains one of the most viable routes to large scale quantum information processing. In contrast, passive error correction relies on the natural physical dynamics of a system to protect encoded quantum information. However, the search is ongoing for a completely satisfactory passive scheme applicable to locally interacting two-dimensional systems. Here, we investigate dynamical decoders that provide passive error correction by embedding the decoding process into local dynamics. We propose a specific discrete time cellular-automaton decoder in the fault tolerant setting and provide numerical evidence showing that the logical qubit has a survival time extended by several orders of magnitude over that of a bare unencoded qubit. We stress that (asynchronous) dynamical decoding gives rise to a Markovian dissipative process. We hence equate cellular-automaton decoding to a fully dissipative topological quantum memory, which removes errors continuously. In this sense, uncontrolled and unwanted local noise can be corrected for by a controlled local dissipative process. We analyze the required resources, commenting on additional polylogarithmic factors beyond those incurred by an ideal constant resource dynamical decoder. (paper)

  9. Cellular automaton and elastic net for event reconstruction in the NEMO-2 experiment

    International Nuclear Information System (INIS)

    Kovalenko, V.

    1997-01-01

    A cellular automaton for track searching and an elastic net for charged particle trajectory fitting are presented. The advantages of the methods are: simplicity of the algorithms, fast and stable convergence to real tracks, and a reconstruction efficiency close to 100%. Demonstration programs are available at http://nuweb.jinr.dubna.su/LNP/NEMO using a Java enabled browser. (orig.)

  10. Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms

    International Nuclear Information System (INIS)

    Wang Xiaohu; Xu Daoyi

    2009-01-01

    In this paper, the global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms is considered. By establishing an integro-differential inequality with impulsive initial condition and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, several new sufficient conditions are obtained to ensure the global exponential stability of the equilibrium point for fuzzy cellular neural networks with delays and reaction-diffusion terms. These results extend and improve the earlier publications. Two examples are given to illustrate the efficiency of the obtained results.

  11. Application of a cellular automaton for the evolution of etched nuclear tracks

    International Nuclear Information System (INIS)

    Cruz-Trujillo, Leonardo de la; Hernández-Hernández, C.; Vázquez-López, C.; Zendejas-Leal, B.E.; Golzarri, I.; Espinosa, G.

    2013-01-01

    In the present work, it is demonstrated the first application of cellular automata to the growing of etched nuclear tracks. The simplest case in which conical etched tracks are gradually formed is presented, as well as a general case of time varying etching rate V t . It is demonstrated that the cellular automata elements consist in an image pattern of the latent nuclear track input cells, 16 rules for updating states, the Moore neighborhood and an algorithm of four states. - Highlights: ► We model the evolution of an etched nuclear track using cellular automata (ca). ► A cellular automaton of a conical track has 4 states and 16 transition rules. ► The ca of general tracks require a not regular mesh and the L(t) and V b parameters

  12. Modeling and Experimental Study of Soft Error Propagation Based on Cellular Automaton

    OpenAIRE

    He, Wei; Wang, Yueke; Xing, Kefei; Yang, Jianwei

    2016-01-01

    Aiming to estimate SEE soft error performance of complex electronic systems, a soft error propagation model based on cellular automaton is proposed and an estimation methodology based on circuit partitioning and error propagation is presented. Simulations indicate that different fault grade jamming and different coupling factors between cells are the main parameters influencing the vulnerability of the system. Accelerated radiation experiments have been developed to determine the main paramet...

  13. Simulation of emotional contagion using modified SIR model: A cellular automaton approach

    Science.gov (United States)

    Fu, Libi; Song, Weiguo; Lv, Wei; Lo, Siuming

    2014-07-01

    Emotion plays an important role in the decision-making of individuals in some emergency situations. The contagion of emotion may induce either normal or abnormal consolidated crowd behavior. This paper aims to simulate the dynamics of emotional contagion among crowds by modifying the epidemiological SIR model to a cellular automaton approach. This new cellular automaton model, entitled the “CA-SIRS model”, captures the dynamic process ‘susceptible-infected-recovered-susceptible', which is based on SIRS contagion in epidemiological theory. Moreover, in this new model, the process is integrated with individual movement. The simulation results of this model show that multiple waves and dynamical stability around a mean value will appear during emotion spreading. It was found that the proportion of initial infected individuals had little influence on the final stable proportion of infected population in a given system, and that infection frequency increased with an increase in the average crowd density. Our results further suggest that individual movement accelerates the spread speed of emotion and increases the stable proportion of infected population. Furthermore, decreasing the duration of an infection and the probability of reinfection can markedly reduce the number of infected individuals. It is hoped that this study will be helpful in crowd management and evacuation organization.

  14. Cellular automaton and elastic net for event reconstruction in the NEMO-2 experiment

    International Nuclear Information System (INIS)

    Kisel, I.; Kovalenko, V.; Laplanche, F.

    1997-01-01

    A cellular automaton for track searching combined with an elastic net for charged particle trajectory fitting is presented. The advantages of the methods are: the simplicity of the algorithms, the fast and stable convergency to real tracks, and a good reconstruction efficiency. The combination of techniques have been used with success for event reconstruction on the data of the NEMO-2 double-beta (ββ) decay experiments. (orig.)

  15. Update schemes of multi-velocity floor field cellular automaton for pedestrian dynamics

    Science.gov (United States)

    Luo, Lin; Fu, Zhijian; Cheng, Han; Yang, Lizhong

    2018-02-01

    Modeling pedestrian movement is an interesting problem both in statistical physics and in computational physics. Update schemes of cellular automaton (CA) models for pedestrian dynamics govern the schedule of pedestrian movement. Usually, different update schemes make the models behave in different ways, which should be carefully recalibrated. Thus, in this paper, we investigated the influence of four different update schemes, namely parallel/synchronous scheme, random scheme, order-sequential scheme and shuffled scheme, on pedestrian dynamics. The multi-velocity floor field cellular automaton (FFCA) considering the changes of pedestrians' moving properties along walking paths and heterogeneity of pedestrians' walking abilities was used. As for parallel scheme only, the collisions detection and resolution should be considered, resulting in a great difference from any other update schemes. For pedestrian evacuation, the evacuation time is enlarged, and the difference in pedestrians' walking abilities is better reflected, under parallel scheme. In face of a bottleneck, for example a exit, using a parallel scheme leads to a longer congestion period and a more dispersive density distribution. The exit flow and the space-time distribution of density and velocity have significant discrepancies under four different update schemes when we simulate pedestrian flow with high desired velocity. Update schemes may have no influence on pedestrians in simulation to create tendency to follow others, but sequential and shuffled update scheme may enhance the effect of pedestrians' familiarity with environments.

  16. Cellular automaton model in the fundamental diagram approach reproducing the synchronized outflow of wide moving jams

    International Nuclear Information System (INIS)

    Tian, Jun-fang; Yuan, Zhen-zhou; Jia, Bin; Fan, Hong-qiang; Wang, Tao

    2012-01-01

    Velocity effect and critical velocity are incorporated into the average space gap cellular automaton model [J.F. Tian, et al., Phys. A 391 (2012) 3129], which was able to reproduce many spatiotemporal dynamics reported by the three-phase theory except the synchronized outflow of wide moving jams. The physics of traffic breakdown has been explained. Various congested patterns induced by the on-ramp are reproduced. It is shown that the occurrence of synchronized outflow, free outflow of wide moving jams is closely related with drivers time delay in acceleration at the downstream jam front and the critical velocity, respectively. -- Highlights: ► Velocity effect is added into average space gap cellular automaton model. ► The physics of traffic breakdown has been explained. ► The probabilistic nature of traffic breakdown is simulated. ► Various congested patterns induced by the on-ramp are reproduced. ► The occurrence of synchronized outflow of jams depends on drivers time delay.

  17. Cellular automaton modelling of ductile iron microstructure in the thin wall casting

    International Nuclear Information System (INIS)

    Burbelko, A A; Gurgul, D; Kapturkiewicz, W; Górny, M

    2012-01-01

    The mathematical model of the globular eutectic solidification in 2D was designed. Proposed model is based on the Cellular Automaton Finite Differences (CA-FD) calculation method. Model has been used for studies of the primary austenite and of globular eutectic grains growth during the ductile iron solidification in the thin wall casting. Model takes into account, among other things, non-uniform temperature distribution in the casting wall cross-section, kinetics of the austenite and graphite grains nucleation, and non-equilibrium nature of the interphase boundary migration.

  18. Remodelling of cellular excitation (reaction) and intercellular coupling (diffusion) by chronic atrial fibrillation represented by a reaction-diffusion system

    Science.gov (United States)

    Zhang, Henggui; Garratt, Clifford J.; Kharche, Sanjay; Holden, Arun V.

    2009-06-01

    Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.

  19. Motzkin numbers out of Random Domino Automaton

    Energy Technology Data Exchange (ETDEWEB)

    Białecki, Mariusz, E-mail: bialecki@igf.edu.pl [Institute of Geophysics, Polish Academy of Sciences, ul. Ks. Janusza 64, 01-452 Warszawa (Poland)

    2012-10-01

    Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton. -- Highlights: ► Motzkin numbers are derived from stochastic cellular automaton with avalanches. ► Explicit solution of toy model of earthquakes is presented. ► Case with inverse-power distribution of avalanches is found.

  20. Modeling and Experimental Study of Soft Error Propagation Based on Cellular Automaton

    Directory of Open Access Journals (Sweden)

    Wei He

    2016-01-01

    Full Text Available Aiming to estimate SEE soft error performance of complex electronic systems, a soft error propagation model based on cellular automaton is proposed and an estimation methodology based on circuit partitioning and error propagation is presented. Simulations indicate that different fault grade jamming and different coupling factors between cells are the main parameters influencing the vulnerability of the system. Accelerated radiation experiments have been developed to determine the main parameters for raw soft error vulnerability of the module and coupling factors. Results indicate that the proposed method is feasible.

  1. Detector independent cellular automaton algorithm for track reconstruction

    Energy Technology Data Exchange (ETDEWEB)

    Kisel, Ivan; Kulakov, Igor; Zyzak, Maksym [Goethe Univ. Frankfurt am Main (Germany); Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH (Germany); Collaboration: CBM-Collaboration

    2013-07-01

    Track reconstruction is one of the most challenging problems of data analysis in modern high energy physics (HEP) experiments, which have to process per second of the order of 10{sup 7} events with high track multiplicity and density, registered by detectors of different types and, in many cases, located in non-homogeneous magnetic field. Creation of reconstruction package common for all experiments is considered to be important in order to consolidate efforts. The cellular automaton (CA) track reconstruction approach has been used successfully in many HEP experiments. It is very simple, efficient, local and parallel. Meanwhile it is intrinsically independent of detector geometry and good candidate for common track reconstruction. The CA implementation for the CBM experiment has been generalized and applied to the ALICE ITS and STAR HFT detectors. Tests with simulated collisions have been performed. The track reconstruction efficiencies are at the level of 95% for majority of the signal tracks for all detectors.

  2. Wavefront cellular learning automata.

    Science.gov (United States)

    Moradabadi, Behnaz; Meybodi, Mohammad Reza

    2018-02-01

    This paper proposes a new cellular learning automaton, called a wavefront cellular learning automaton (WCLA). The proposed WCLA has a set of learning automata mapped to a connected structure and uses this structure to propagate the state changes of the learning automata over the structure using waves. In the WCLA, after one learning automaton chooses its action, if this chosen action is different from the previous action, it can send a wave to its neighbors and activate them. Each neighbor receiving the wave is activated and must choose a new action. This structure for the WCLA is necessary in many dynamic areas such as social networks, computer networks, grid computing, and web mining. In this paper, we introduce the WCLA framework as an optimization tool with diffusion capability, study its behavior over time using ordinary differential equation solutions, and present its accuracy using expediency analysis. To show the superiority of the proposed WCLA, we compare the proposed method with some other types of cellular learning automata using two benchmark problems.

  3. Wavefront cellular learning automata

    Science.gov (United States)

    Moradabadi, Behnaz; Meybodi, Mohammad Reza

    2018-02-01

    This paper proposes a new cellular learning automaton, called a wavefront cellular learning automaton (WCLA). The proposed WCLA has a set of learning automata mapped to a connected structure and uses this structure to propagate the state changes of the learning automata over the structure using waves. In the WCLA, after one learning automaton chooses its action, if this chosen action is different from the previous action, it can send a wave to its neighbors and activate them. Each neighbor receiving the wave is activated and must choose a new action. This structure for the WCLA is necessary in many dynamic areas such as social networks, computer networks, grid computing, and web mining. In this paper, we introduce the WCLA framework as an optimization tool with diffusion capability, study its behavior over time using ordinary differential equation solutions, and present its accuracy using expediency analysis. To show the superiority of the proposed WCLA, we compare the proposed method with some other types of cellular learning automata using two benchmark problems.

  4. Application of a cellular automaton for recognition of straight tracks in the spectrometer DISTO

    International Nuclear Information System (INIS)

    Bussa, M.P.; Fava, L.; Ferrero, L.; Grasso, A.; Ivanov, V.V.; Kisel', I.V.; Konotopskaya, E.V.; Pontecorvo, G.B.

    1995-01-01

    A model of the cellular automaton for recognition of straight tracks has been developed. The program realization of this algorithm has shown high efficiency and speed for the simulated data for the experiment DISTO. Its working speed provides for the processing of approximately 1000 events/sec using the 50 MIPS RISC-processor. This makes suitable its application for track recognition in the second level trigger of the DISTO spectrometer. 10 refs., 7 figs., 1 tab

  5. An intrinsic poperty of memory of the Cellular automaton infrastructure of Nature leading to the organization of the physical world as an Internet o things; TOE = IOT

    Science.gov (United States)

    Berkovich, Simon

    2015-04-01

    The undamental advantage of a Cellular automaton construction foris that it can be viewed as an undetectable absolute frame o reference, in accordance with Lorentz-Poincare's interpretation.. The cellular automaton model for physical poblems comes upon two basic hurdles: (1) How to find the Elemental Rule that, and how to get non-locality from local transformations. Both problems are resolved considering the transfomation rule of mutual distributed synchronization Actually any information proessing device starts with a clocking system. and it turns out that ``All physical phenomena are different aspects of the high-level description of distributed mutual synchronization in a network of digital clocks''. Non-locality comes from two hugely different time-scales of signaling.. The universe is acombinines information and matter processes, These fast spreading diffusion wave solutions create the mechanism of the Holographic Universe. And thirdly Disengaged from synchronization, circular counters can perform memory functions by retaining phases of their oscillations, an idea of Von Neumann'. Thus, the suggested model generates the necessary constructs for the physical world as an Internet of Things. Life emerges due to the specifics of macromolecules that serve as communication means, with the holographic memory...

  6. Cellular automata models for diffusion of information and highway traffic flow

    Science.gov (United States)

    Fuks, Henryk

    In the first part of this work we study a family of deterministic models for highway traffic flow which generalize cellular automaton rule 184. This family is parameterized by the speed limit m and another parameter k that represents degree of 'anticipatory driving'. We compare two driving strategies with identical maximum throughput: 'conservative' driving with high speed limit and 'anticipatory' driving with low speed limit. Those two strategies are evaluated in terms of accident probability. We also discuss fundamental diagrams of generalized traffic rules and examine limitations of maximum achievable throughput. Possible modifications of the model are considered. For rule 184, we present exact calculations of the order parameter in a transition from the moving phase to the jammed phase using the method of preimage counting, and use this result to construct a solution to the density classification problem. In the second part we propose a probabilistic cellular automaton model for the spread of innovations, rumors, news, etc., in a social system. We start from simple deterministic models, for which exact expressions for the density of adopters are derived. For a more realistic model, based on probabilistic cellular automata, we study the influence of a range of interaction R on the shape of the adoption curve. When the probability of adoption is proportional to the local density of adopters, and individuals can drop the innovation with some probability p, the system exhibits a second order phase transition. Critical line separating regions of parameter space in which asymptotic density of adopters is positive from the region where it is equal to zero converges toward the mean-field line when the range of the interaction increases. In a region between R=1 critical line and the mean-field line asymptotic density of adopters depends on R, becoming zero if R is too small (smaller than some critical value). This result demonstrates the importance of connectivity in

  7. Cellular automaton modeling of ductile iron microstructure in the thin wall

    Directory of Open Access Journals (Sweden)

    A.A. Burbelko

    2011-10-01

    Full Text Available The mathematical model of the globular eutectic solidification in 2D was designed. Proposed model is based on the Cellular Automaton Finite Differences (CA-FD calculation method. Model has been used for studies of the primary austenite and of globular eutectic grains growth during the solidification of the ductile iron with different carbon equivalent in the thin wall casting. Model takes into account, among other things, non-uniform temperature distribution in the casting wall cross-section, kinetics of the austenite and graphite grains nucleation, and non-equilibrium nature of the interphase boundary migration. Solidification of the DI with different carbon equivalents was analyzed. Obtained results were compared with the solidification path calculated by CALPHAD method.

  8. Reaction-Diffusion Automata Phenomenology, Localisations, Computation

    CERN Document Server

    Adamatzky, Andrew

    2013-01-01

    Reaction-diffusion and excitable media are amongst most intriguing substrates. Despite apparent simplicity of the physical processes involved the media exhibit a wide range of amazing patterns: from target and spiral waves to travelling localisations and stationary breathing patterns. These media are at the heart of most natural processes, including morphogenesis of living beings, geological formations, nervous and muscular activity, and socio-economic developments.   This book explores a minimalist paradigm of studying reaction-diffusion and excitable media using locally-connected networks of finite-state machines: cellular automata and automata on proximity graphs. Cellular automata are marvellous objects per se because they show us how to generate and manage complexity using very simple rules of dynamical transitions. When combined with the reaction-diffusion paradigm the cellular automata become an essential user-friendly tool for modelling natural systems and designing future and emergent computing arch...

  9. Cellular automaton simulation of counter flow with paired pedestrians

    Directory of Open Access Journals (Sweden)

    Hui Xiong

    2011-12-01

    Full Text Available Knowledge on pedestrian behavior is the basis to build decision support system for crowd evacuation management in emergency. In this paper, the impact of paired walking behavior on pedestrian counter flow in a channel is studied. The pedestrian walking behaviors are simulated by the cellular automaton model and the pedestrians are classified as single right walker, single left walker, paired right walker, and paired left walker. Single walker can move forward, leftward, rightward or stand still. The paired pedestrians are considered as a combined unit similar to the single walker in terms of route choice and they can move to the same direction simultaneously. It is found that flow and velocity decrease with increase of the paired rate in case of stable density. Simulation results reveal the phase transitions in terms of density from free flow to the unstable flow and from the unstable flow to the congestion flow. However, the critical densities of phase transition are unaffected by the channel size.

  10. Modelling for Near-Surface Transport Dynamics of Hydrogen of Plasma Facing Materials by use of Cellular Automaton

    International Nuclear Information System (INIS)

    Shimura, K.; Terai, T.; Yamawaki, M.

    2003-01-01

    In this study, the kinetics of desorption of adsorbed hydrogen from an ideal metallic surface is modelled in Cellular Automaton (CA). The modelling is achieved by downgrading the surface to one dimension. The model consists of two parts that are surface migration and desorption. The former is attained by randomly sorting the particles at each time, the latter is realised by modelling the thermally-activated process. For the verification of this model, thermal desorption is simulated then the comparison with the chemical kinetics is carried out. Excellent agreement is observed from the result. The results show that this model is reasonable to express the recombinative desorption of two chemisorbed adatoms. Though, the application of this model is limited to the second-order reaction case. But it can be believed that the groundwork of modelling the transport dynamics of hydrogen through the surface under complex conditions is established

  11. Development of a formalism of movable cellular automaton method for numerical modeling of fracture of heterogeneous elastic-plastic materials

    Directory of Open Access Journals (Sweden)

    S. Psakhie

    2013-04-01

    Full Text Available A general approach to realization of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of particle-based numerical methods is proposed in the paper. It is based on building many-body forces of particle interaction, which provide response of particle ensemble correctly conforming to the response (including elastic-plastic behavior and fracture of simulated solids. Implementation of proposed approach within particle-based methods is demonstrated by the example of the movable cellular automaton (MCA method, which integrates the possibilities of particle-based discrete element method (DEM and cellular automaton methods. Emergent advantages of the developed approach to formulation of many-body interaction are discussed. Main of them are its applicability to various realizations of the concept of discrete elements and a possibility to realize various rheological models (including elastic-plastic or visco-elastic-plastic and models of fracture to study deformation and fracture of solid-phase materials and media. Capabilities of particle-based modeling of heterogeneous solids are demonstrated by the problem of simulation of deformation and fracture of particle-reinforced metal-ceramic composites.

  12. 4D Cellular Automaton Track Finder in the CBM Experiment

    International Nuclear Information System (INIS)

    Akishina, Valentina; Kisel, Ivan

    2016-01-01

    The CBM experiment (FAIR/GSI, Darmstadt, Germany) will focus on the measurement of rare probes at interaction rates up to 10MHz with data flow of up to 1 TB/s. It requires a novel read-out and data-acquisition concept with self-triggered electronics and free-streaming data. In this case resolving different collisions is a non-trivial task and event building must be performed in software online. That requires full online event reconstruction and selection not only in space, but also in time, so-called 4D event building and selection. This is a task of the First-Level Event Selection (FLES). The FLES reconstruction and selection package consists of several modules: track finding, track fitting, short-lived particles finding, event building and event selection. The Cellular Automaton (CA) track finder algorithm was adapted towards time-based reconstruction. In this article, we describe in detail the modification done to the algorithm, as well as the performance of the developed time-based CA approach

  13. A new stochastic cellular automaton model on traffic flow and its jamming phase transition

    International Nuclear Information System (INIS)

    Sakai, Satoshi; Nishinari, Katsuhiro; Iida, Shinji

    2006-01-01

    A general stochastic traffic cellular automaton (CA) model, which includes the slow-to-start effect and driver's perspective, is proposed in this paper. It is shown that this model includes well-known traffic CA models such as the Nagel-Schreckenberg model, the quick-start model and the slow-to-start model as specific cases. Fundamental diagrams of this new model clearly show metastable states around the critical density even when the stochastic effect is present. We also obtain analytic expressions of the phase transition curve in phase diagrams by using approximate flow-density relations at boundaries. These phase transition curves are in excellent agreement with numerical results

  14. Non-linearity and spatial resolution in a cellular automaton model of a small upland basin

    Directory of Open Access Journals (Sweden)

    T. J. Coulthard

    1998-01-01

    Full Text Available The continuing development of computational fluid dynamics is allowing the high resolution study of hydraulic and sediment transport processes but, due to computational complexities, these are rarely applied to areas larger than a reach. Existing approaches, based upon linked cross sections, can give a quasi two-dimensional view, effectively simulating sediment transport for a single river reach. However, a basin represents a whole discrete dynamic system within which channel, floodplain and slope processes operate over a wide range of space and time scales. Here, a cellular automaton (CA approach has been used to overcome some of these difficulties, in which the landscape is represented as a series of fixed size cells. For every model iteration, each cell acts only in relation to the influence of its immediate neighbours in accordance with appropriate rules. The model presented here takes approximations of existing flow and sediment transport equations, and integrates them, together with slope and floodplain approximations, within a cellular automaton framework. This method has been applied to the basin of Cam Gill Beck (4.2 km2 above Starbotton, upper Wharfedale, a tributary of the River Wharfe, North Yorkshire, UK. This approach provides, for the first time, a workable model of the whole basin at a 1 m resolution. Preliminary results show the evolution of bars, braids, terraces and alluvial fans which are similar to those observed in the field, and examples of large and small scale non-linear behaviour which may have considerable implications for future models.

  15. Cellular automaton simulation of pedestrian counter flow with different walk velocities

    International Nuclear Information System (INIS)

    Weng, W. G.; Chen, T.; Yuan, H. Y.; Fan, W. C.

    2006-01-01

    This paper presents a cellular automaton model without step back for pedestrian dynamics considering the human behaviors which can make judgments in some complex situations. This model can simulate pedestrian movement with different walk velocities through update at different time-step intervals. Two kinds of boundary conditions including periodic and open boundary for pedestrian counter flow are considered, and their dynamical characteristics are discussed. Simulation results show that for periodic boundary condition there are three phases of pedestrian patterns, i.e., freely moving phase, lane formation phase, and perfectly stopped phase at some certain total density ranges. In the stage of lane formation, the phenomenon that pedestrians exceed those with lower walk velocity through a narrow walkway can be found. For open boundary condition, at some certain entrance densities, there are two steady states of pedestrian patterns; but the first is metastable. Spontaneous fluctuations can break the first steady state, i.e., freely moving phase, and run into the second steady state, i.e., perfectly stopped phase

  16. Some Properties of topological pressure on cellular automata

    Directory of Open Access Journals (Sweden)

    Chih-Hung Chang

    2014-09-01

    Full Text Available This paper investigates the ergodicity and the power rule of the topological pressure of a cellular automaton. If a cellular automaton is either leftmost or rightmost premutive (due to the terminology given by Hedlund [Math.~Syst.~Theor.~3, 320-375, 1969], then it is ergodic with respect to the uniform Bernoulli measure. More than that, the relation of topological pressure between the original cellular automaton and its power rule is expressed in a closed form. As an application, the topological pressure of a linear cellular automaton can be computed explicitly.

  17. CATS: a cellular automaton for tracking in silicon for the HERA-B vertex detector

    International Nuclear Information System (INIS)

    Abt, I.; Emeliyanov, D.; Kisel, I.; Masciocchi, S.

    2002-01-01

    The new track reconstruction program CATS developed for the Vertex Detector System of the HERA-B experiment at DESY is presented. It employs a cellular automaton for track searching and the Kalman filter for track fitting. This results in a very fast algorithm that combines highly efficient track recognition with accurate and reliable track parameter estimation. To reduce the computational cost of the fit an optimized numerical implementation of the Kalman filter is used. Alternative approaches to the track reconstruction in the VDS are also discussed. Since 1999, after extensive tests on simulated data, CATS has been employed to reconstruct experimental data collected in HERA-B. Results regarding tracking performance, the accuracy of track parameter estimates and CPU time consumption are presented

  18. Zeno's paradox in quantum cellular automata

    Energy Technology Data Exchange (ETDEWEB)

    Groessing, G [Atominst. der Oesterreichischen Universitaeten, Vienna (Austria); Zeilinger, A [Inst. fuer Experimentalphysik, Univ. Innsbruck (Austria)

    1991-07-01

    The effect of Zeno's paradox in quantum theory is demonstrated with the aid of quantum mechanical cellular automata. It is shown that the degree of non-unitarity of the cellular automaton evolution and the frequency of consecutive measurements of cellular automaton states are operationally indistinguishable. (orig.).

  19. Zeno's paradox in quantum cellular automata

    International Nuclear Information System (INIS)

    Groessing, G.; Zeilinger, A.

    1991-01-01

    The effect of Zeno's paradox in quantum theory is demonstrated with the aid of quantum mechanical cellular automata. It is shown that the degree of non-unitarity of the cellular automaton evolution and the frequency of consecutive measurements of cellular automaton states are operationally indistinguishable. (orig.)

  20. Parallel 4-Dimensional Cellular Automaton Track Finder for the CBM Experiment

    International Nuclear Information System (INIS)

    Akishina, Valentina; Kisel, Ivan

    2016-01-01

    The CBM experiment (FAIR/GSI, Darmstadt, Germany) will focus on the measurement of rare probes at interaction rates up to 10 MHz with data flow of up to 1 TB/s. It requires a novel read-out and data-acquisition concept with self-triggered electronics and free-streaming data. In this case resolving different collisions is not a trivial task and event building must be performed in software online. That requires full online event reconstruction and selection not only in space, but also in time, so-called 4D event building and selection. This is a task of the First-Level Event Selection (FLES). The FLES reconstruction and selection package consists of several modules: track finding, track fitting, short-lived particles finding, event building and event selection. The Cellular Automaton (CA) track finder algorithm was adapted towards time-slice-based reconstruction and included into the CBMROOT framework. In this article, we describe the modification done to the algorithm, as well as the performance of the developed time-based approach. (paper)

  1. Cellular Automaton Modeling of Dendritic Growth Using a Multi-grid Method

    International Nuclear Information System (INIS)

    Natsume, Y; Ohsasa, K

    2015-01-01

    A two-dimensional cellular automaton model with a multi-grid method was developed to simulate dendritic growth. In the present model, we used a triple-grid system for temperature, solute concentration and solid fraction fields as a new approach of the multi-grid method. In order to evaluate the validity of the present model, we carried out simulations of single dendritic growth, secondary dendrite arm growth, multi-columnar dendritic growth and multi-equiaxed dendritic growth. From the results of the grid dependency from the simulation of single dendritic growth, we confirmed that the larger grid can be used in the simulation and that the computational time can be reduced dramatically. In the simulation of secondary dendrite arm growth, the results from the present model were in good agreement with the experimental data and the simulated results from a phase-field model. Thus, the present model can quantitatively simulate dendritic growth. From the simulated results of multi-columnar and multi-equiaxed dendrites, we confirmed that the present model can perform simulations under practical solidification conditions. (paper)

  2. Cellular automaton simulation examining progenitor hierarchy structure effects on mammary ductal carcinoma in situ.

    Science.gov (United States)

    Bankhead, Armand; Magnuson, Nancy S; Heckendorn, Robert B

    2007-06-07

    A computer simulation is used to model ductal carcinoma in situ, a form of non-invasive breast cancer. The simulation uses known histological morphology, cell types, and stochastic cell proliferation to evolve tumorous growth within a duct. The ductal simulation is based on a hybrid cellular automaton design using genetic rules to determine each cell's behavior. The genetic rules are a mutable abstraction that demonstrate genetic heterogeneity in a population. Our goal was to examine the role (if any) that recently discovered mammary stem cell hierarchies play in genetic heterogeneity, DCIS initiation and aggressiveness. Results show that simpler progenitor hierarchies result in greater genetic heterogeneity and evolve DCIS significantly faster. However, the more complex progenitor hierarchy structure was able to sustain the rapid reproduction of a cancer cell population for longer periods of time.

  3. Reaction-diffusion systems in intracellular molecular transport and control.

    Science.gov (United States)

    Soh, Siowling; Byrska, Marta; Kandere-Grzybowska, Kristiana; Grzybowski, Bartosz A

    2010-06-07

    Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. Most research to date has focused on active-transport mechanisms, although passive diffusion is often equally rapid and energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction-diffusion (RD) systems that control a wide range of cellular functions-from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. These apparently diverse systems share many common features and are "wired" according to "generic" motifs such as nonlinear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport-kinetic equations or, at least on a qualitative level, of the characteristic times of the constituent subprocesses. Therefore, in reviewing the manifestations of cellular RD, we also describe basic theory of reaction-diffusion phenomena.

  4. Multiscale modeling of porous ceramics using movable cellular automaton method

    Science.gov (United States)

    Smolin, Alexey Yu.; Smolin, Igor Yu.; Smolina, Irina Yu.

    2017-10-01

    The paper presents a multiscale model for porous ceramics based on movable cellular automaton method, which is a particle method in novel computational mechanics of solid. The initial scale of the proposed approach corresponds to the characteristic size of the smallest pores in the ceramics. At this scale, we model uniaxial compression of several representative samples with an explicit account of pores of the same size but with the unique position in space. As a result, we get the average values of Young's modulus and strength, as well as the parameters of the Weibull distribution of these properties at the current scale level. These data allow us to describe the material behavior at the next scale level were only the larger pores are considered explicitly, while the influence of small pores is included via effective properties determined earliar. If the pore size distribution function of the material has N maxima we need to perform computations for N-1 levels in order to get the properties step by step from the lowest scale up to the macroscale. The proposed approach was applied to modeling zirconia ceramics with bimodal pore size distribution. The obtained results show correct behavior of the model sample at the macroscale.

  5. Equiaxed and columnar dendrite growth simulation in Al-7Si- Mg ternary alloys using cellular automaton method

    International Nuclear Information System (INIS)

    Chen, Rui; Xu, Qingyan; Liu, Baicheng

    2015-01-01

    In this paper, a modified cellular automaton (MCA) model allowing for the prediction of dendrite growth of Al-Si-Mg ternary alloys in two and three dimensions is presented. The growth kinetic of S/L interface is calculated based on the solute equilibrium approach. In order to describe the dendrite growth with arbitrarily crystallographic orientations, this model introduces a modified decentered octahedron algorithm for neighborhood tracking to eliminate the effect of mesh dependency on dendrite growth. The thermody namic and kinetic data needed for dendrite growth is obtained through coupling with Pandat software package in combination with thermodynamic/kinetic/equilibrium phase diagram calculation databases. The effect of interactions between various alloying elements on solute diffusion coefficient is considered in the model. This model has first been used to simulate Al-7Si (weight percent) binary dendrite growth followed by a validation using theoretical predictions. For ternary alloy, Al-7Si-0.5Mg dendrite simulation has been carried out and the effects of solute interactions on diffusion matrix as well as the differences of Si and Mg in solute distribution have been analyzed. For actual application, this model has been applied to simulate the equiaxed dendrite growth with various crystallographic orientations of Al-7Si-0.36Mg ternary alloy, and the predicted secondary dendrite arm spacing (SDAS) shows a reasonable agreement with the experimental ones. Furthermore, the columnar dendrite growth in directional solidification has also been simulated and the predicted primary dendrite arm spacing (PDAS) is in good agreement with experiments. The simulated results effectively demonstrate the abilities of the model in prediction of dendritic microstructure of Al-Si-Mg ternary alloy. (paper)

  6. Equiaxed and columnar dendrite growth simulation in Al-7Si- Mg ternary alloys using cellular automaton method

    Science.gov (United States)

    Chen, Rui; Xu, Qingyan; Liu, Baicheng

    2015-06-01

    In this paper, a modified cellular automaton (MCA) model allowing for the prediction of dendrite growth of Al-Si-Mg ternary alloys in two and three dimensions is presented. The growth kinetic of S/L interface is calculated based on the solute equilibrium approach. In order to describe the dendrite growth with arbitrarily crystallographic orientations, this model introduces a modified decentered octahedron algorithm for neighborhood tracking to eliminate the effect of mesh dependency on dendrite growth. The thermody namic and kinetic data needed for dendrite growth is obtained through coupling with Pandat software package in combination with thermodynamic/kinetic/equilibrium phase diagram calculation databases. The effect of interactions between various alloying elements on solute diffusion coefficient is considered in the model. This model has first been used to simulate Al-7Si (weight percent) binary dendrite growth followed by a validation using theoretical predictions. For ternary alloy, Al-7Si-0.5Mg dendrite simulation has been carried out and the effects of solute interactions on diffusion matrix as well as the differences of Si and Mg in solute distribution have been analyzed. For actual application, this model has been applied to simulate the equiaxed dendrite growth with various crystallographic orientations of Al-7Si-0.36Mg ternary alloy, and the predicted secondary dendrite arm spacing (SDAS) shows a reasonable agreement with the experimental ones. Furthermore, the columnar dendrite growth in directional solidification has also been simulated and the predicted primary dendrite arm spacing (PDAS) is in good agreement with experiments. The simulated results effectively demonstrate the abilities of the model in prediction of dendritic microstructure of Al-Si-Mg ternary alloy.

  7. Parallel 4-dimensional cellular automaton track finder for the CBM experiment

    Energy Technology Data Exchange (ETDEWEB)

    Akishina, Valentina [Goethe-Universitaet Frankfurt am Main, Frankfurt am Main (Germany); Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); JINR Joint Institute for Nuclear Research, Dubna (Russian Federation); Kisel, Ivan [Goethe-Universitaet Frankfurt am Main, Frankfurt am Main (Germany); Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Collaboration: CBM-Collaboration

    2016-07-01

    The CBM experiment at FAIR will focus on the measurement of rare probes at interaction rates up to 10 MHz. The beam will provide free stream of particles, so that information about different collisions may overlap in time. It requires the full online event reconstruction not only in space, but also in time, so-called 4D (4-dimensional) event building. This is a task of the First-Level Event Selection (FLES) package. The FLES reconstruction package consists of several modules: track finding, track fitting, short-lived particles finding, event building and selection. The Silicon Tracking System (STS) time measurement information was included into the Cellular Automaton (CA) track finder algorithm. The 4D track finder algorithm speed (8.5 ms per event in a time-slice) and efficiency is comparable with the event-based analysis. The CA track finder was fully parallelised inside the time-slice. The parallel version achieves a speed-up factor of 10.6 while parallelising between 10 Intel Xeon physical cores with a hyper-threading. The first version of event building based on 4D track finder was implemented.

  8. A Modified Cellular Automaton Approach for Mixed Bicycle Traffic Flow Modeling

    Directory of Open Access Journals (Sweden)

    Xiaonian Shan

    2015-01-01

    Full Text Available Several previous studies have used the Cellular Automaton (CA for the modeling of bicycle traffic flow. However, previous CA models have several limitations, resulting in differences between the simulated and the observed traffic flow features. The primary objective of this study is to propose a modified CA model for simulating the characteristics of mixed bicycle traffic flow. Field data were collected on physically separated bicycle path in Shanghai, China, and were used to calibrate the CA model using the genetic algorithm. Traffic flow features between simulations of several CA models and field observations were compared. The results showed that our modified CA model produced more accurate simulation for the fundamental diagram and the passing events in mixed bicycle traffic flow. Based on our model, the bicycle traffic flow features, including the fundamental diagram, the number of passing events, and the number of lane changes, were analyzed. We also analyzed the traffic flow features with different traffic densities, traffic components on different travel lanes. Results of the study can provide important information for understanding and simulating the operations of mixed bicycle traffic flow.

  9. Time scale of diffusion in molecular and cellular biology

    International Nuclear Information System (INIS)

    Holcman, D; Schuss, Z

    2014-01-01

    Diffusion is the driver of critical biological processes in cellular and molecular biology. The diverse temporal scales of cellular function are determined by vastly diverse spatial scales in most biophysical processes. The latter are due, among others, to small binding sites inside or on the cell membrane or to narrow passages between large cellular compartments. The great disparity in scales is at the root of the difficulty in quantifying cell function from molecular dynamics and from simulations. The coarse-grained time scale of cellular function is determined from molecular diffusion by the mean first passage time of molecular Brownian motion to a small targets or through narrow passages. The narrow escape theory (NET) concerns this issue. The NET is ubiquitous in molecular and cellular biology and is manifested, among others, in chemical reactions, in the calculation of the effective diffusion coefficient of receptors diffusing on a neuronal cell membrane strewn with obstacles, in the quantification of the early steps of viral trafficking, in the regulation of diffusion between the mother and daughter cells during cell division, and many other cases. Brownian trajectories can represent the motion of a molecule, a protein, an ion in solution, a receptor in a cell or on its membrane, and many other biochemical processes. The small target can represent a binding site or an ionic channel, a hidden active site embedded in a complex protein structure, a receptor for a neurotransmitter on the membrane of a neuron, and so on. The mean time to attach to a receptor or activator determines diffusion fluxes that are key regulators of cell function. This review describes physical models of various subcellular microdomains, in which the NET coarse-grains the molecular scale to a higher cellular-level, thus clarifying the role of cell geometry in determining subcellular function. (topical review)

  10. Time scale of diffusion in molecular and cellular biology

    Science.gov (United States)

    Holcman, D.; Schuss, Z.

    2014-05-01

    Diffusion is the driver of critical biological processes in cellular and molecular biology. The diverse temporal scales of cellular function are determined by vastly diverse spatial scales in most biophysical processes. The latter are due, among others, to small binding sites inside or on the cell membrane or to narrow passages between large cellular compartments. The great disparity in scales is at the root of the difficulty in quantifying cell function from molecular dynamics and from simulations. The coarse-grained time scale of cellular function is determined from molecular diffusion by the mean first passage time of molecular Brownian motion to a small targets or through narrow passages. The narrow escape theory (NET) concerns this issue. The NET is ubiquitous in molecular and cellular biology and is manifested, among others, in chemical reactions, in the calculation of the effective diffusion coefficient of receptors diffusing on a neuronal cell membrane strewn with obstacles, in the quantification of the early steps of viral trafficking, in the regulation of diffusion between the mother and daughter cells during cell division, and many other cases. Brownian trajectories can represent the motion of a molecule, a protein, an ion in solution, a receptor in a cell or on its membrane, and many other biochemical processes. The small target can represent a binding site or an ionic channel, a hidden active site embedded in a complex protein structure, a receptor for a neurotransmitter on the membrane of a neuron, and so on. The mean time to attach to a receptor or activator determines diffusion fluxes that are key regulators of cell function. This review describes physical models of various subcellular microdomains, in which the NET coarse-grains the molecular scale to a higher cellular-level, thus clarifying the role of cell geometry in determining subcellular function.

  11. A parallelized three-dimensional cellular automaton model for grain growth during additive manufacturing

    Science.gov (United States)

    Lian, Yanping; Lin, Stephen; Yan, Wentao; Liu, Wing Kam; Wagner, Gregory J.

    2018-05-01

    In this paper, a parallelized 3D cellular automaton computational model is developed to predict grain morphology for solidification of metal during the additive manufacturing process. Solidification phenomena are characterized by highly localized events, such as the nucleation and growth of multiple grains. As a result, parallelization requires careful treatment of load balancing between processors as well as interprocess communication in order to maintain a high parallel efficiency. We give a detailed summary of the formulation of the model, as well as a description of the communication strategies implemented to ensure parallel efficiency. Scaling tests on a representative problem with about half a billion cells demonstrate parallel efficiency of more than 80% on 8 processors and around 50% on 64; loss of efficiency is attributable to load imbalance due to near-surface grain nucleation in this test problem. The model is further demonstrated through an additive manufacturing simulation with resulting grain structures showing reasonable agreement with those observed in experiments.

  12. A parallelized three-dimensional cellular automaton model for grain growth during additive manufacturing

    Science.gov (United States)

    Lian, Yanping; Lin, Stephen; Yan, Wentao; Liu, Wing Kam; Wagner, Gregory J.

    2018-01-01

    In this paper, a parallelized 3D cellular automaton computational model is developed to predict grain morphology for solidification of metal during the additive manufacturing process. Solidification phenomena are characterized by highly localized events, such as the nucleation and growth of multiple grains. As a result, parallelization requires careful treatment of load balancing between processors as well as interprocess communication in order to maintain a high parallel efficiency. We give a detailed summary of the formulation of the model, as well as a description of the communication strategies implemented to ensure parallel efficiency. Scaling tests on a representative problem with about half a billion cells demonstrate parallel efficiency of more than 80% on 8 processors and around 50% on 64; loss of efficiency is attributable to load imbalance due to near-surface grain nucleation in this test problem. The model is further demonstrated through an additive manufacturing simulation with resulting grain structures showing reasonable agreement with those observed in experiments.

  13. 3D simulation of friction stir welding based on movable cellular automaton method

    Science.gov (United States)

    Eremina, Galina M.

    2017-12-01

    The paper is devoted to a 3D computer simulation of the peculiarities of material flow taking place in friction stir welding (FSW). The simulation was performed by the movable cellular automaton (MCA) method, which is a representative of particle methods in mechanics. Commonly, the flow of material in FSW is simulated based on computational fluid mechanics, assuming the material as continuum and ignoring its structure. The MCA method considers a material as an ensemble of bonded particles. The rupture of interparticle bonds and the formation of new bonds enable simulations of crack nucleation and healing as well as mas mixing and microwelding. The simulation results showed that using pins of simple shape (cylinder, cone, and pyramid) without a shoulder results in small displacements of plasticized material in workpiece thickness directions. Nevertheless, the optimal ratio of longitudinal velocity to rotational speed makes it possible to transport the welded material around the pin several times and to produce a joint of good quality.

  14. Probabilistic cellular automata.

    Science.gov (United States)

    Agapie, Alexandru; Andreica, Anca; Giuclea, Marius

    2014-09-01

    Cellular automata are binary lattices used for modeling complex dynamical systems. The automaton evolves iteratively from one configuration to another, using some local transition rule based on the number of ones in the neighborhood of each cell. With respect to the number of cells allowed to change per iteration, we speak of either synchronous or asynchronous automata. If randomness is involved to some degree in the transition rule, we speak of probabilistic automata, otherwise they are called deterministic. With either type of cellular automaton we are dealing with, the main theoretical challenge stays the same: starting from an arbitrary initial configuration, predict (with highest accuracy) the end configuration. If the automaton is deterministic, the outcome simplifies to one of two configurations, all zeros or all ones. If the automaton is probabilistic, the whole process is modeled by a finite homogeneous Markov chain, and the outcome is the corresponding stationary distribution. Based on our previous results for the asynchronous case-connecting the probability of a configuration in the stationary distribution to its number of zero-one borders-the article offers both numerical and theoretical insight into the long-term behavior of synchronous cellular automata.

  15. Cellular Automaton Study of Hydrogen Porosity Evolution Coupled with Dendrite Growth During Solidification in the Molten Pool of Al-Cu Alloys

    Science.gov (United States)

    Gu, Cheng; Wei, Yanhong; Yu, Fengyi; Liu, Xiangbo; She, Lvbo

    2017-09-01

    Welding porosity defects significantly reduce the mechanical properties of welded joints. In this paper, the hydrogen porosity evolution coupled with dendrite growth during solidification in the molten pool of Al-4.0 wt pct Cu alloy was modeled and simulated. Three phases, including a liquid phase, a solid phase, and a gas phase, were considered in this model. The growth of dendrites and hydrogen gas pores was reproduced using a cellular automaton (CA) approach. The diffusion of solute and hydrogen was calculated using the finite difference method (FDM). Columnar and equiaxed dendrite growth with porosity evolution were simulated. Competitive growth between different dendrites and porosities was observed. Dendrite morphology was influenced by porosity formation near dendrites. After solidification, when the porosities were surrounded by dendrites, they could not escape from the liquid, and they made pores that existed in the welded joints. With the increase in the cooling rate, the average diameter of porosities decreased, and the average number of porosities increased. The average diameter of porosities and the number of porosities in the simulation results had the same trend as the experimental results.

  16. Multiscale Simulation of Porous Ceramics Based on Movable Cellular Automaton Method

    Science.gov (United States)

    Smolin, A.; Smolin, I.; Eremina, G.; Smolina, I.

    2017-10-01

    The paper presents a model for simulating mechanical behaviour of multiscale porous ceramics based on movable cellular automaton method, which is a novel particle method in computational mechanics of solid. The initial scale of the proposed approach corresponds to the characteristic size of the smallest pores in the ceramics. At this scale, we model uniaxial compression of several representative samples with an explicit account of pores of the same size but with the random unique position in space. As a result, we get the average values of Young’s modulus and strength, as well as the parameters of the Weibull distribution of these properties at the current scale level. These data allow us to describe the material behaviour at the next scale level were only the larger pores are considered explicitly, while the influence of small pores is included via the effective properties determined at the previous scale level. If the pore size distribution function of the material has N maxima we need to perform computations for N - 1 levels in order to get the properties from the lowest scale up to the macroscale step by step. The proposed approach was applied to modelling zirconia ceramics with bimodal pore size distribution. The obtained results show correct behaviour of the model sample at the macroscale.

  17. Simulation of glioblastoma multiforme (GBM) tumor cells using ising model on the Creutz Cellular Automaton

    Science.gov (United States)

    Züleyha, Artuç; Ziya, Merdan; Selçuk, Yeşiltaş; Kemal, Öztürk M.; Mesut, Tez

    2017-11-01

    Computational models for tumors have difficulties due to complexity of tumor nature and capacities of computational tools, however, these models provide visions to understand interactions between tumor and its micro environment. Moreover computational models have potential to develop strategies for individualized treatments for cancer. To observe a solid brain tumor, glioblastoma multiforme (GBM), we present a two dimensional Ising Model applied on Creutz cellular automaton (CCA). The aim of this study is to analyze avascular spherical solid tumor growth, considering transitions between non tumor cells and cancer cells are like phase transitions in physical system. Ising model on CCA algorithm provides a deterministic approach with discrete time steps and local interactions in position space to view tumor growth as a function of time. Our simulation results are given for fixed tumor radius and they are compatible with theoretical and clinic data.

  18. Macroscopic Spatial Complexity of the Game of Life Cellular Automaton: A Simple Data Analysis

    Science.gov (United States)

    Hernández-Montoya, A. R.; Coronel-Brizio, H. F.; Rodríguez-Achach, M. E.

    In this chapter we present a simple data analysis of an ensemble of 20 time series, generated by averaging the spatial positions of the living cells for each state of the Game of Life Cellular Automaton (GoL). We show that at the macroscopic level described by these time series, complexity properties of GoL are also presented and the following emergent properties, typical of data extracted complex systems such as financial or economical come out: variations of the generated time series following an asymptotic power law distribution, large fluctuations tending to be followed by large fluctuations, and small fluctuations tending to be followed by small ones, and fast decay of linear correlations, however, the correlations associated to their absolute variations exhibit a long range memory. Finally, a Detrended Fluctuation Analysis (DFA) of the generated time series, indicates that the GoL spatial macro states described by the time series are not either completely ordered or random, in a measurable and very interesting way.

  19. Scaling, phase transitions, and nonuniversality in a self-organized critical cellular-automaton model

    International Nuclear Information System (INIS)

    Christensen, K.; Olami, Z.

    1992-01-01

    We present a two-dimensional continuous cellular automaton that is equivalent to a driven spring-block model. Both the conservation and the anisotropy in the model are controllable quantities. Above a critical level of conservation, the model exhibits self-organized criticality. The self-organization of this system and hence the critical exponents depend on the conservation and the boundary conditions. In the critical isotropic nonconservative phase, the exponents change continuously as a function of conservation. Furthermore, the exponents vary continuously when changing the boundary conditions smoothly. Consequently, there is no universality of the critical exponents. We discuss the relevance of this for earthquakes. Introducing anisotropy changes the scaling of the distribution function, but not the power-law exponent. We explore the phase diagram of this model. We find that at low conservation levels a localization transition occurs. We see two additional phase transitions. The first is seen when moving from the conservative into the nonconservative model. The second appears when passing from the anisotropic two-dimensional system to the purely one-dimensional system

  20. Stable oscillations of a predator-prey probabilistic cellular automaton: a mean-field approach

    International Nuclear Information System (INIS)

    Tome, Tania; Carvalho, Kelly C de

    2007-01-01

    We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the Lotka-Volterra model. Two levels of mean-field approximations are set up. The simple approximation is equivalent to an extended patch model, a simple metapopulation model with patches colonized by prey, patches colonized by predators and empty patches. This approximation is capable of describing the limited available space for species occupancy. The pair approximation is moreover able to describe two types of coexistence of prey and predators: one where population densities are constant in time and another displaying self-sustained time oscillations of the population densities. The oscillations are associated with limit cycles and arise through a Hopf bifurcation. They are stable against changes in the initial conditions and, in this sense, they differ from the Lotka-Volterra cycles which depend on initial conditions. In this respect, the present model is biologically more realistic than the Lotka-Volterra model

  1. Anomalous spreading of a density front from an infinite continuous source in a concentration-dependent lattice gas automaton diffusion model

    CERN Document Server

    Kuentz, M

    2003-01-01

    A two-dimensional lattice gas automaton (LGA) is used for simulating concentration-dependent diffusion in a microscopically random heterogeneous structure. The heterogeneous medium is initialized at a low density rho sub 0 and then submitted to a steep concentration gradient by continuous injection of particles at a concentration rho sub 1 >rho sub 0 from a one-dimensional source to model spreading of a density front. Whereas the nonlinear diffusion equation generally used to describe concentration-dependent diffusion processes predicts a scaling law of the type phi = xt sup - sup 1 sup / sup 2 in one dimension, the spreading process is shown to deviate from the expected t sup 1 sup / sup 2 scaling. The time exponent is found to be larger than 1/2, i.e. diffusion of the density front is enhanced with respect to standard Fickian diffusion. It is also established that the anomalous time exponent decreases as time elapses: anomalous spreading is thus not a timescaling process. We demonstrate that occurrence of a...

  2. A cellular automaton - finite volume method for the simulation of dendritic and eutectic growth in binary alloys using an adaptive mesh refinement

    Science.gov (United States)

    Dobravec, Tadej; Mavrič, Boštjan; Šarler, Božidar

    2017-11-01

    A two-dimensional model to simulate the dendritic and eutectic growth in binary alloys is developed. A cellular automaton method is adopted to track the movement of the solid-liquid interface. The diffusion equation is solved in the solid and liquid phases by using an explicit finite volume method. The computational domain is divided into square cells that can be hierarchically refined or coarsened using an adaptive mesh based on the quadtree algorithm. Such a mesh refines the regions of the domain near the solid-liquid interface, where the highest concentration gradients are observed. In the regions where the lowest concentration gradients are observed the cells are coarsened. The originality of the work is in the novel, adaptive approach to the efficient and accurate solution of the posed multiscale problem. The model is verified and assessed by comparison with the analytical results of the Lipton-Glicksman-Kurz model for the steady growth of a dendrite tip and the Jackson-Hunt model for regular eutectic growth. Several examples of typical microstructures are simulated and the features of the method as well as further developments are discussed.

  3. Recursive definition of global cellular-automata mappings

    DEFF Research Database (Denmark)

    Feldberg, Rasmus; Knudsen, Carsten; Rasmussen, Steen

    1994-01-01

    A method for a recursive definition of global cellular-automata mappings is presented. The method is based on a graphical representation of global cellular-automata mappings. For a given cellular-automaton rule the recursive algorithm defines the change of the global cellular-automaton mapping...... as the number of lattice sites is incremented. A proof of lattice size invariance of global cellular-automata mappings is derived from an approximation to the exact recursive definition. The recursive definitions are applied to calculate the fractal dimension of the set of reachable states and of the set...

  4. Microtubule self-organisation by reaction-diffusion processes causes collective transport and organisation of cellular particles

    Directory of Open Access Journals (Sweden)

    Demongeot Jacques

    2004-06-01

    Full Text Available Abstract Background The transport of intra-cellular particles by microtubules is a major biological function. Under appropriate in vitro conditions, microtubule preparations behave as a 'complex' system and show 'emergent' phenomena. In particular, they form dissipative structures that self-organise over macroscopic distances by a combination of reaction and diffusion. Results Here, we show that self-organisation also gives rise to a collective transport of colloidal particles along a specific direction. Particles, such as polystyrene beads, chromosomes, nuclei, and vesicles are carried at speeds of several microns per minute. The process also results in the macroscopic self-organisation of these particles. After self-organisation is completed, they show the same pattern of organisation as the microtubules. Numerical simulations of a population of growing and shrinking microtubules, incorporating experimentally realistic reaction dynamics, predict self-organisation. They forecast that during self-organisation, macroscopic parallel arrays of oriented microtubules form which cross the reaction space in successive waves. Such travelling waves are capable of transporting colloidal particles. The fact that in the simulations, the aligned arrays move along the same direction and at the same speed as the particles move, suggest that this process forms the underlying mechanism for the observed transport properties. Conclusions This process constitutes a novel physical chemical mechanism by which chemical energy is converted into collective transport of colloidal particles along a given direction. Self-organisation of this type provides a new mechanism by which intra cellular particles such as chromosomes and vesicles can be displaced and simultaneously organised by microtubules. It is plausible that processes of this type occur in vivo.

  5. Microtubule self-organisation by reaction-diffusion processes causes collective transport and organisation of cellular particles

    Science.gov (United States)

    Glade, Nicolas; Demongeot, Jacques; Tabony, James

    2004-01-01

    Background The transport of intra-cellular particles by microtubules is a major biological function. Under appropriate in vitro conditions, microtubule preparations behave as a 'complex' system and show 'emergent' phenomena. In particular, they form dissipative structures that self-organise over macroscopic distances by a combination of reaction and diffusion. Results Here, we show that self-organisation also gives rise to a collective transport of colloidal particles along a specific direction. Particles, such as polystyrene beads, chromosomes, nuclei, and vesicles are carried at speeds of several microns per minute. The process also results in the macroscopic self-organisation of these particles. After self-organisation is completed, they show the same pattern of organisation as the microtubules. Numerical simulations of a population of growing and shrinking microtubules, incorporating experimentally realistic reaction dynamics, predict self-organisation. They forecast that during self-organisation, macroscopic parallel arrays of oriented microtubules form which cross the reaction space in successive waves. Such travelling waves are capable of transporting colloidal particles. The fact that in the simulations, the aligned arrays move along the same direction and at the same speed as the particles move, suggest that this process forms the underlying mechanism for the observed transport properties. Conclusions This process constitutes a novel physical chemical mechanism by which chemical energy is converted into collective transport of colloidal particles along a given direction. Self-organisation of this type provides a new mechanism by which intra cellular particles such as chromosomes and vesicles can be displaced and simultaneously organised by microtubules. It is plausible that processes of this type occur in vivo. PMID:15176973

  6. A study of intergranular corrosion of austenitic stainless steel by electrochemical potentiodynamic reactivation, electron back-scattering diffraction and cellular automaton

    Energy Technology Data Exchange (ETDEWEB)

    Yu Xiaofei [Department of Chemistry, Shandong University, Jinan 250100 (China); Chen Shenhao [Department of Chemistry, Shandong University, Jinan 250100 (China); State Key Laboratory for Corrosion and Protection, Shenyang 110016 (China)], E-mail: shchen@sdu.edu.cn; Liu Ying; Ren Fengfeng [Department of Chemistry, Shandong University, Jinan 250100 (China)

    2010-06-15

    The impact of solution and sensitization treatments on the intergranular corrosion (IGC) of austenitic stainless steel (316) was studied by electrochemical potentiodynamic reactivation (EPR) test, and the results showed the degree of sensitization (DOS) decreased as solution treatment temperature and time went up, but it increased as sensitization temperature prolonged. Factors that affected IGC were investigated by field emission scanning electron microscope (FE-SEM) and electron back-scattering diffraction (EBSD). Furthermore, the precipitation evolution of Cr-rich carbides and the distribution of chromium concentration were simulated by cellular automaton (CA), clearly showing the effects of solution and sensitization treatments on IGC.

  7. An Asynchronous Recurrent Network of Cellular Automaton-Based Neurons and Its Reproduction of Spiking Neural Network Activities.

    Science.gov (United States)

    Matsubara, Takashi; Torikai, Hiroyuki

    2016-04-01

    Modeling and implementation approaches for the reproduction of input-output relationships in biological nervous tissues contribute to the development of engineering and clinical applications. However, because of high nonlinearity, the traditional modeling and implementation approaches encounter difficulties in terms of generalization ability (i.e., performance when reproducing an unknown data set) and computational resources (i.e., computation time and circuit elements). To overcome these difficulties, asynchronous cellular automaton-based neuron (ACAN) models, which are described as special kinds of cellular automata that can be implemented as small asynchronous sequential logic circuits have been proposed. This paper presents a novel type of such ACAN and a theoretical analysis of its excitability. This paper also presents a novel network of such neurons, which can mimic input-output relationships of biological and nonlinear ordinary differential equation model neural networks. Numerical analyses confirm that the presented network has a higher generalization ability than other major modeling and implementation approaches. In addition, Field-Programmable Gate Array-implementations confirm that the presented network requires lower computational resources.

  8. Recursive definition of global cellular-automata mappings

    International Nuclear Information System (INIS)

    Feldberg, R.; Knudsen, C.; Rasmussen, S.

    1994-01-01

    A method for a recursive definition of global cellular-automata mappings is presented. The method is based on a graphical representation of global cellular-automata mappings. For a given cellular-automaton rule the recursive algorithm defines the change of the global cellular-automaton mapping as the number of lattice sites is incremented. A proof of lattice size invariance of global cellular-automata mappings is derived from an approximation to the exact recursive definition. The recursive definitions are applied to calculate the fractal dimension of the set of reachable states and of the set of fixed points of cellular automata on an infinite lattice

  9. fA cellular automaton model of crystalline cellulose hydrolysis by cellulases

    Directory of Open Access Journals (Sweden)

    Little Bryce A

    2011-10-01

    Full Text Available Abstract Background Cellulose from plant biomass is an abundant, renewable material which could be a major feedstock for low emissions transport fuels such as cellulosic ethanol. Cellulase enzymes that break down cellulose into fermentable sugars are composed of different types - cellobiohydrolases I and II, endoglucanase and β-glucosidase - with separate functions. They form a complex interacting network between themselves, soluble hydrolysis product molecules, solution and solid phase substrates and inhibitors. There have been many models proposed for enzymatic saccharification however none have yet employed a cellular automaton approach, which allows important phenomena, such as enzyme crowding on the surface of solid substrates, denaturation and substrate inhibition, to be considered in the model. Results The Cellulase 4D model was developed de novo taking into account the size and composition of the substrate and surface-acting enzymes were ascribed behaviors based on their movements, catalytic activities and rates, affinity for, and potential for crowding of, the cellulose surface, substrates and inhibitors, and denaturation rates. A basic case modeled on literature-derived parameters obtained from Trichoderma reesei cellulases resulted in cellulose hydrolysis curves that closely matched curves obtained from published experimental data. Scenarios were tested in the model, which included variation of enzyme loadings, adsorption strengths of surface acting enzymes and reaction periods, and the effect on saccharide production over time was assessed. The model simulations indicated an optimal enzyme loading of between 0.5 and 2 of the base case concentrations where a balance was obtained between enzyme crowding on the cellulose crystal, and that the affinities of enzymes for the cellulose surface had a large effect on cellulose hydrolysis. In addition, improvements to the cellobiohydrolase I activity period substantially improved overall

  10. Simulation of Microstructure during Laser Rapid Forming Solidification Based on Cellular Automaton

    Directory of Open Access Journals (Sweden)

    Zhi-jian Wang

    2014-01-01

    Full Text Available The grain microstructure of molten pool during the solidification of TC4 titanium alloy in the single point laser cladding was investigated based on the CAFE model which is the cellular automaton (CA coupled with the finite element (FE method. The correct temperature field is the prerequisite for simulating the grain microstructure during the solidification of the molten pool. The model solves the energy equation by the FE method to simulate the temperature distribution in the molten pool of the single point laser cladding. Based on the temperature field, the solidification microstructure of the molten pool is also simulated with the CAFE method. The results show that the maximum temperature in the molten pool increases with the laser power and the scanning rate. The laser power has a larger influence on the temperature distribution of the molten pool than the scanning rate. During the solidification of the molten pool, the heat at the bottom of the molten pool transfers faster than that at the top of the molten pool. The grains rapidly grow into the molten pool, and then the columnar crystals are formed. This study has a very important significance for improving the quality of the structure parts manufactured through the laser cladding forming.

  11. Cellular automaton for migration in ecosystem: Application of traffic model to a predator-prey system

    Science.gov (United States)

    Nagatani, Takashi; Tainaka, Kei-ichi

    2018-01-01

    In most cases, physicists have studied the migration of biospecies by the use of random walk. In the present article, we apply cellular automaton of traffic model. For simplicity, we deal with an ecosystem contains a prey and predator, and use one-dimensional lattice with two layers. Preys stay on the first layer, but predators uni-directionally move on the second layer. The spatial and temporal evolution is numerically explored. It is shown that the migration has the important effect on populations of both prey and predator. Without migration, the phase transition between a prey-phase and coexisting-phase occurs. In contrast, the phase transition disappears by migration. This is because predator can survive due to migration. We find another phase transition for spatial distribution: in one phase, prey and predator form a stripe pattern of condensation and rarefaction, while in the other phase, they uniformly distribute. The self-organized stripe may be similar to the migration patterns in real ecosystems.

  12. TWO-DIMENSIONAL CELLULAR AUTOMATON MODEL FOR THE EVOLUTION OF ACTIVE REGION CORONAL PLASMAS

    Energy Technology Data Exchange (ETDEWEB)

    López Fuentes, Marcelo [Instituto de Astronomía y Física del Espacio, CONICET-UBA, CC. 67, Suc. 28, 1428 Buenos Aires (Argentina); Klimchuk, James A., E-mail: lopezf@iafe.uba.ar [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States)

    2015-02-01

    We study a two-dimensional cellular automaton (CA) model for the evolution of coronal loop plasmas. The model is based on the idea that coronal loops are made of elementary magnetic strands that are tangled and stressed by the displacement of their footpoints by photospheric motions. The magnetic stress accumulated between neighbor strands is released in sudden reconnection events or nanoflares that heat the plasma. We combine the CA model with the Enthalpy Based Thermal Evolution of Loops model to compute the response of the plasma to the heating events. Using the known response of the X-Ray Telescope on board Hinode, we also obtain synthetic data. The model obeys easy-to-understand scaling laws relating the output (nanoflare energy, temperature, density, intensity) to the input parameters (field strength, strand length, critical misalignment angle). The nanoflares have a power-law distribution with a universal slope of –2.5, independent of the input parameters. The repetition frequency of nanoflares, expressed in terms of the plasma cooling time, increases with strand length. We discuss the implications of our results for the problem of heating and evolution of active region coronal plasmas.

  13. A new cellular automaton for signal controlled traffic flow based on driving behaviors

    Science.gov (United States)

    Wang, Yang; Chen, Yan-Yan

    2015-03-01

    The complexity of signal controlled traffic largely stems from the various driving behaviors developed in response to the traffic signal. However, the existing models take a few driving behaviors into account and consequently the traffic dynamics has not been completely explored. Therefore, a new cellular automaton model, which incorporates the driving behaviors typically manifesting during the different stages when the vehicles are moving toward a traffic light, is proposed in this paper. Numerical simulations have demonstrated that the proposed model can produce the spontaneous traffic breakdown and the dissolution of the over-saturated traffic phenomena. Furthermore, the simulation results indicate that the slow-to-start behavior and the inch-forward behavior can foster the traffic breakdown. Particularly, it has been discovered that the over-saturated traffic can be revised to be an under-saturated state when the slow-down behavior is activated after the spontaneous breakdown. Finally, the contributions of the driving behaviors on the traffic breakdown have been examined. Project supported by the National Basic Research Program of China (Grand No. 2012CB723303) and the Beijing Committee of Science and Technology, China (Grand No. Z1211000003120100).

  14. A NANOFLARE-BASED CELLULAR AUTOMATON MODEL AND THE OBSERVED PROPERTIES OF THE CORONAL PLASMA

    Energy Technology Data Exchange (ETDEWEB)

    Fuentes, Marcelo López [Instituto de Astronomía y Física del Espacio, CONICET-UBA, CC. 67, Suc. 28, 1428 Buenos Aires (Argentina); Klimchuk, James A., E-mail: lopezf@iafe.uba.ar [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States)

    2016-09-10

    We use the cellular automaton model described in López Fuentes and Klimchuk to study the evolution of coronal loop plasmas. The model, based on the idea of a critical misalignment angle in tangled magnetic fields, produces nanoflares of varying frequency with respect to the plasma cooling time. We compare the results of the model with active region (AR) observations obtained with the Hinode /XRT and SDO /AIA instruments. The comparison is based on the statistical properties of synthetic and observed loop light curves. Our results show that the model reproduces the main observational characteristics of the evolution of the plasma in AR coronal loops. The typical intensity fluctuations have amplitudes of 10%–15% both for the model and the observations. The sign of the skewness of the intensity distributions indicates the presence of cooling plasma in the loops. We also study the emission measure (EM) distribution predicted by the model and obtain slopes in log(EM) versus log(T) between 2.7 and 4.3, in agreement with published observational values.

  15. A Nanoflare-Based Cellular Automaton Model and the Observed Properties of the Coronal Plasma

    Science.gov (United States)

    Lopez-Fuentes, Marcelo; Klimchuk, James Andrew

    2016-01-01

    We use the cellular automaton model described in Lopez Fuentes and Klimchuk to study the evolution of coronal loop plasmas. The model, based on the idea of a critical misalignment angle in tangled magnetic fields, produces nanoflares of varying frequency with respect to the plasma cooling time. We compare the results of the model with active region (AR) observations obtained with the Hinode/XRT and SDOAIA instruments. The comparison is based on the statistical properties of synthetic and observed loop light curves. Our results show that the model reproduces the main observational characteristics of the evolution of the plasma in AR coronal loops. The typical intensity fluctuations have amplitudes of 10 percent - 15 percent both for the model and the observations. The sign of the skewness of the intensity distributions indicates the presence of cooling plasma in the loops. We also study the emission measure (EM) distribution predicted by the model and obtain slopes in log(EM) versus log(T) between 2.7 and 4.3, in agreement with published observational values.

  16. The MatchIT Automaton

    DEFF Research Database (Denmark)

    Weyland, Mathias; Fellermann, Harold; Hadorn, Maik

    2013-01-01

    In this paper, we propose the MATCHIT Automaton (MA), a theoretical framework that shows how to improve the yield of the synthesis of chemical polymer reactions. This is achieved by separating sub-steps of the path of syn- thesis into compartments. We use chemical containers (chemtainers) to carr...... reticulum and the Golgi apparatus, and we show how this compartmentalization can be exploited for the synthesis of branched polymers. Lastly, we show exam- ples of artificial branched polymers and discuss how the MA can be configured to synthesize them with maximal yield....

  17. Reaction-diffusion fronts with inhomogeneous initial conditions

    Energy Technology Data Exchange (ETDEWEB)

    Bena, I [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Droz, M [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Martens, K [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Racz, Z [Institute for Theoretical Physics, Eoetvoes University, 1117 Budapest (Hungary)

    2007-02-14

    Properties of reaction zones resulting from A+B {yields} C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic inhomogeneity in the distribution of the B species. For simple two-dimensional geometries, exact analytical results are presented for the time evolution of the geometric shape of the front. We also show using cellular automata simulations that the fluctuations can be neglected both in the shape and in the width of the front.

  18. Simple cellular automaton model for traffic breakdown, highway capacity, and synchronized flow

    Science.gov (United States)

    Kerner, Boris S.; Klenov, Sergey L.; Schreckenberg, Michael

    2011-10-01

    We present a simple cellular automaton (CA) model for two-lane roads explaining the physics of traffic breakdown, highway capacity, and synchronized flow. The model consists of the rules “acceleration,” “deceleration,” “randomization,” and “motion” of the Nagel-Schreckenberg CA model as well as “overacceleration through lane changing to the faster lane,” “comparison of vehicle gap with the synchronization gap,” and “speed adaptation within the synchronization gap” of Kerner's three-phase traffic theory. We show that these few rules of the CA model can appropriately simulate fundamental empirical features of traffic breakdown and highway capacity found in traffic data measured over years in different countries, like characteristics of synchronized flow, the existence of the spontaneous and induced breakdowns at the same bottleneck, and associated probabilistic features of traffic breakdown and highway capacity. Single-vehicle data derived in model simulations show that synchronized flow first occurs and then self-maintains due to a spatiotemporal competition between speed adaptation to a slower speed of the preceding vehicle and passing of this slower vehicle. We find that the application of simple dependences of randomization probability and synchronization gap on driving situation allows us to explain the physics of moving synchronized flow patterns and the pinch effect in synchronized flow as observed in real traffic data.

  19. A cellular automaton method to simulate the microstructure and evolution of low-enriched uranium (LEU) U–Mo/Al dispersion type fuel plates

    Energy Technology Data Exchange (ETDEWEB)

    Drera, Saleem S., E-mail: saleem.drera@gmail.com [Mechanical Engineering, Colorado School of Mines, Golden, CO 80401 (United States); Hofman, Gerard L. [Argonne National Laboratory, Chicago, IL 60439 (United States); Kee, Robert J. [Mechanical Engineering, Colorado School of Mines, Golden, CO 80401 (United States); King, Jeffrey C. [Metallurgical and Materials Engineering, Colorado School of Mines, Golden, CO 80401 (United States)

    2014-10-15

    Highlights: • This article presents a cellular automata (CA) algorithm to synthesize the growth of intermetallic interaction layers in U–Mo/Al dispersion fuel. • The method utilizes a 3D representation of the fuel, which is discretized into separate voxels that can change identy based on derived CA rules. • The CA model is compared to ILT measurements for RERTR experimental data. • The primary objective of the model is to synthesize three-dimensional microstructures that can be used in subsequent thermal and mechanical modeling. • The CA model can be used for predictive analysis. For example, it can be used to study the dependence of temperature on interaction layer growth. - Abstract: Low-enriched uranium (LEU) fuel plates for high power materials test reactors (MTR) are composed of nominally spherical uranium–molybdenum (U–Mo) particles within an aluminum matrix. Fresh U–Mo particles typically range between 10 and 100 μm in diameter, with particle volume fractions up to 50%. As the fuel ages, reaction–diffusion processes cause the formation and growth of interaction layers that surround the fuel particles. The growth rate depends upon the temperature and radiation environment. The cellular automaton algorithm described in this paper can synthesize realistic random fuel-particle structures and simulate the growth of the intermetallic interaction layers. Examples in the present paper pack approximately 1000 particles into three-dimensional rectangular fuel structures that are approximately 1 mm on each side. The computational approach is designed to yield synthetic microstructures consistent with images from actual fuel plates and is validated by comparison with empirical data on actual fuel plates.

  20. Towards modeling of random lasing in dye doped bio-organic based systems: ray-tracing and cellular automaton analysis

    Science.gov (United States)

    Mitus, A. C.; Stopa, P.; Zaklukiewicz, W.; Pawlik, G.; Mysliwiec, J.; Kajzar, F.; Rau, I.

    2015-08-01

    One of many photonic applications of biopolymers as functional materials is random lasing resulting from an incorporation of highly luminescent dyes into biopolymeric matrix, which leads to a random but coherent light scattering in amplifying medium. In spite of numerous theoretical and experimental studies the origin of the coherence is still not clear and various scenarios are discussed. In particular, inhomogeneity of biopolymeric layers can hypothetically promote the feedback in the scattering of the emitted light resulting in coherent and incoherent random lasing. In this paper we analyze the light scattering in a model system of scattering centers of circular shapes and various dimensions using ray-tracing techniques. In the second part, which has mostly a tutorial character, we present the approach to the study of random lasing using a cellular automaton model of Wiersma et al.

  1. Statistical mechanics of cellular automata

    International Nuclear Information System (INIS)

    Wolfram, S.

    1983-01-01

    Cellular automata are used as simple mathematical models to investigate self-organization in statistical mechanics. A detailed analysis is given of ''elementary'' cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to p definite rules involving the values of its nearest neighbors. With simple initial configurations, the cellular automata either tend to homogeneous states, or generate self-similar patterns with fractal dimensions approx. =1.59 or approx. =1.69. With ''random'' initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization phenomena. Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules. More complicated cellular automata are briefly considered, and connections with dynamical systems theory and the formal theory of computation are discussed

  2. A New Cellular Automaton Method Coupled with a Rate-dependent (CARD) Model for Predicting Dynamic Recrystallization Behavior

    Science.gov (United States)

    Azarbarmas, M.; Aghaie-Khafri, M.

    2018-03-01

    A comprehensive cellular automaton (CA) model should be coupled with a rate-dependent (RD) model for analyzing the RD deformation of alloys at high temperatures. In the present study, a new CA technique coupled with an RD model—namely, CARD—was developed. The proposed CARD model was used to simulate the dynamic recrystallization phenomenon during the hot deformation of the Inconel 718 superalloy. This model is capable of calculating the mean grain size and volume fraction of dynamic recrystallized grains, and estimating the phenomenological flow behavior of the material. In the presented model, an actual orientation definition comprising three Euler angles was used by implementing the electron backscatter diffraction data. For calculating the lattice rotation of grains, it was assumed that all slip systems of grains are active during the high-temperature deformation because of the intrinsic rate dependency of the procedure. Moreover, the morphological changes in grains were obtained using a topological module.

  3. Simulating bi-directional pedestrian flow in a cellular automaton model considering the body-turning behavior

    Science.gov (United States)

    Jin, Cheng-Jie; Jiang, Rui; Yin, Jun-Lin; Dong, Li-Yun; Li, Dawei

    2017-09-01

    In the experiments of bi-directional pedestrian flow, it is often observed that pedestrians turn their bodies and change from walking straight to walking sideways, in order to mitigate or avoid the conflicts with opposite walking ones. When these conflicts disappear, pedestrians restore and walk straight again. In the turning states, the forward velocities of pedestrians are not affected. In order to simulate this body-turning behavior, we use a cellular automaton (CA) model named ITP model, which has been proposed before. But the occupied area of one pedestrian is set as 0.4 m∗0.2 m. After the introduction of new rules of turnings and restorations, the pedestrians become more intelligent and flexible during the lane formation process, and some improvements of the fundamental diagram of pedestrian flow can be found. The simulation results of two different scenarios under open boundary conditions are also presented, and compared with the experimental data. It is shown that the new model performs much better than the original model in various tests, which further confirms the validity of the new rules. We think this approach is one useful contribution to the pedestrian flow modeling.

  4. Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

    Science.gov (United States)

    Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

    2018-05-30

    Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

  5. Meredys, a multi-compartment reaction-diffusion simulator using multistate realistic molecular complexes

    Directory of Open Access Journals (Sweden)

    Le Novère Nicolas

    2010-03-01

    Full Text Available Abstract Background Most cellular signal transduction mechanisms depend on a few molecular partners whose roles depend on their position and movement in relation to the input signal. This movement can follow various rules and take place in different compartments. Additionally, the molecules can form transient complexes. Complexation and signal transduction depend on the specific states partners and complexes adopt. Several spatial simulator have been developed to date, but none are able to model reaction-diffusion of realistic multi-state transient complexes. Results Meredys allows for the simulation of multi-component, multi-feature state molecular species in two and three dimensions. Several compartments can be defined with different diffusion and boundary properties. The software employs a Brownian dynamics engine to simulate reaction-diffusion systems at the reactive particle level, based on compartment properties, complex structure, and hydro-dynamic radii. Zeroth-, first-, and second order reactions are supported. The molecular complexes have realistic geometries. Reactive species can contain user-defined feature states which can modify reaction rates and outcome. Models are defined in a versatile NeuroML input file. The simulation volume can be split in subvolumes to speed up run-time. Conclusions Meredys provides a powerful and versatile way to run accurate simulations of molecular and sub-cellular systems, that complement existing multi-agent simulation systems. Meredys is a Free Software and the source code is available at http://meredys.sourceforge.net/.

  6. Predictability in cellular automata.

    Science.gov (United States)

    Agapie, Alexandru; Andreica, Anca; Chira, Camelia; Giuclea, Marius

    2014-01-01

    Modelled as finite homogeneous Markov chains, probabilistic cellular automata with local transition probabilities in (0, 1) always posses a stationary distribution. This result alone is not very helpful when it comes to predicting the final configuration; one needs also a formula connecting the probabilities in the stationary distribution to some intrinsic feature of the lattice configuration. Previous results on the asynchronous cellular automata have showed that such feature really exists. It is the number of zero-one borders within the automaton's binary configuration. An exponential formula in the number of zero-one borders has been proved for the 1-D, 2-D and 3-D asynchronous automata with neighborhood three, five and seven, respectively. We perform computer experiments on a synchronous cellular automaton to check whether the empirical distribution obeys also that theoretical formula. The numerical results indicate a perfect fit for neighbourhood three and five, which opens the way for a rigorous proof of the formula in this new, synchronous case.

  7. Analyzing the Influence of Mobile Phone Use of Drivers on Traffic Flow Based on an Improved Cellular Automaton Model

    Directory of Open Access Journals (Sweden)

    Yao Xiao

    2015-01-01

    Full Text Available This paper aimed to analyze the influence of drivers’ behavior of phone use while driving on traffic flow, including both traffic efficiency and traffic safety. An improved cellular automaton model was proposed to simulate traffic flow with distracted drivers based on the Nagel-Schreckenberg model. The driving characters of drivers using a phone were first discussed and a value representing the probability to use a phone while driving was put into the CA model. Simulation results showed that traffic flow rate was significantly reduced if some drivers used a phone compared to no phone use. The flow rate and velocity decreased as the proportion of drivers using a phone increased. While, under low density, the risk of traffic decreased first and then increased as the distracted drivers increased, the distracted behavior of drivers, like using a phone, could reduce the flow rate by 5 percent according to the simulation.

  8. Diffusive instabilities in hyperbolic reaction-diffusion equations

    Science.gov (United States)

    Zemskov, Evgeny P.; Horsthemke, Werner

    2016-03-01

    We investigate two-variable reaction-diffusion systems of the hyperbolic type. A linear stability analysis is performed, and the conditions for diffusion-driven instabilities are derived. Two basic types of eigenvalues, real and complex, are described. Dispersion curves for both types of eigenvalues are plotted and their behavior is analyzed. The real case is related to the Turing instability, and the complex one corresponds to the wave instability. We emphasize the interesting feature that the wave instability in the hyperbolic equations occurs in two-variable systems, whereas in the parabolic case one needs three reaction-diffusion equations.

  9. Amplitude equations for a sub-diffusive reaction-diffusion system

    International Nuclear Information System (INIS)

    Nec, Y; Nepomnyashchy, A A

    2008-01-01

    A sub-diffusive reaction-diffusion system with a positive definite memory operator and a nonlinear reaction term is analysed. Amplitude equations (Ginzburg-Landau type) are derived for short wave (Turing) and long wave (Hopf) bifurcation points

  10. Diffusion-controlled reaction. V. Effect of concentration-dependent diffusion coefficient on reaction rate in graft polymerization

    International Nuclear Information System (INIS)

    Imre, K.; Odian, G.

    1979-01-01

    The effect of diffusion on radiation-initiated graft polymerization has been studied with emphasis on the single- and two-penetrant cases. When the physical properties of the penetrants are similar, the two-penetrant problems can be reduced to the single-penetrant problem by redefining the characteristic parameters of the system. The diffusion-free graft polymerization rate is assumed to be proportional to the upsilon power of the monomer concentration respectively, and, in which the proportionality constant a = k/sub p/R/sub i//sup w//k/sub t//sup z/, where k/sub p/ and k/sub t/ are the propagation and termination rate constants, respectively, and R/sub i/ is the initiation rate. The values of upsilon, w, and z depend on the particular reaction system. The results of earlier work were generalized by allowing a non-Fickian diffusion rate which predicts an essentially exponential dependence on the monomer concentration of the diffusion coefficient, D = D 0 [exp(deltaC/M)], where M is the saturation concentration. A reaction system is characterized by the three dimensionless parameters, upsilon, delta, and A = (L/2)[aM/sup (upsilon--1)//D 0 ]/sup 1/2/, where L is the polymer film thickness. Graft polymerization tends to become diffusion controlled as A increases. Larger values of delta and ν cause a reaction system to behave closer to the diffusion-free regime. Transition from diffusion-free to diffusion-controlled reaction involves changes in the dependence of the reaction rate on film thickness, initiation rate, and monomer concentration. Although the diffusion-free rate is w order in initiation rate, upsilon order in monomer, and independent of film thickness, the diffusion-controlled rate is w/2 order in initiator rate and inverse first-order in film thickness. Dependence of the diffusion-controlled rate on monomer is dependent in a complex manner on the diffusional characteristics of the reaction system. 11 figures, 4 tables

  11. The Influence of Receptor-Mediated Interactions on Reaction-Diffusion Mechanisms of Cellular Self-organisation

    Czech Academy of Sciences Publication Activity Database

    Klika, Václav; Baker, R. E.; Headon, D.; Gaffney, E. A.

    2012-01-01

    Roč. 74, č. 4 (2012), s. 935-957 ISSN 0092-8240 Institutional research plan: CEZ:AV0Z20760514 Keywords : reaction-diffusion * receptor-mediated patterning * turing models Subject RIV: BO - Biophysics Impact factor: 2.023, year: 2012 http://www.springerlink.com/content/9713544x6871w4n6/?MUD=MP

  12. Intelligent Growth Automaton of Virtual Plant Based on Physiological Engine

    Science.gov (United States)

    Zhu, Qingsheng; Guo, Mingwei; Qu, Hongchun; Deng, Qingqing

    In this paper, a novel intelligent growth automaton of virtual plant is proposed. Initially, this intelligent growth automaton analyzes the branching pattern which is controlled by genes and then builds plant; moreover, it stores the information of plant growth, provides the interface between virtual plant and environment, and controls the growth and development of plant on the basis of environment and the function of plant organs. This intelligent growth automaton can simulate that the plant growth is controlled by genetic information system, and the information of environment and the function of plant organs. The experimental results show that the intelligent growth automaton can simulate the growth of plant conveniently and vividly.

  13. Effect of psychological tension on pedestrian counter flow via an extended cost potential field cellular automaton model

    Science.gov (United States)

    Li, Xingli; Guo, Fang; Kuang, Hua; Zhou, Huaguo

    2017-12-01

    Psychology tells us that the different level of tension may lead to different behavior variation for individuals. In this paper, an extended cost potential field cellular automaton is proposed to simulate pedestrian counter flow under an emergency by considering behavior variation of pedestrian induced by psychological tension. A quantitative formula is introduced to describe behavioral changes caused by psychological tension, which also leads to the increasing cost of discomfort. The numerical simulations are performed under the periodic boundary condition and show that the presented model can capture some essential features of pedestrian counter flow, such as lane formation and segregation phenomenon for normal condition. Furthermore, an interesting feature is found that when pedestrians are in an extremely nervous state, a stable lane formation will be broken by a disordered mixture flow. The psychological nervousness under an emergency is not always negative to moving efficiency and a moderate level of tension will delay the occurrence of jamming phase. In addition, a larger asymmetrical ratio of left walkers to right walkers will improve the critical density related to the jamming phase and retard the occurrence of completely jammed phase. These findings will be helpful in pedestrian control and management under an emergency.

  14. Using exploratory regression to identify optimal driving factors for cellular automaton modeling of land use change.

    Science.gov (United States)

    Feng, Yongjiu; Tong, Xiaohua

    2017-09-22

    Defining transition rules is an important issue in cellular automaton (CA)-based land use modeling because these models incorporate highly correlated driving factors. Multicollinearity among correlated driving factors may produce negative effects that must be eliminated from the modeling. Using exploratory regression under pre-defined criteria, we identified all possible combinations of factors from the candidate factors affecting land use change. Three combinations that incorporate five driving factors meeting pre-defined criteria were assessed. With the selected combinations of factors, three logistic regression-based CA models were built to simulate dynamic land use change in Shanghai, China, from 2000 to 2015. For comparative purposes, a CA model with all candidate factors was also applied to simulate the land use change. Simulations using three CA models with multicollinearity eliminated performed better (with accuracy improvements about 3.6%) than the model incorporating all candidate factors. Our results showed that not all candidate factors are necessary for accurate CA modeling and the simulations were not sensitive to changes in statistically non-significant driving factors. We conclude that exploratory regression is an effective method to search for the optimal combinations of driving factors, leading to better land use change models that are devoid of multicollinearity. We suggest identification of dominant factors and elimination of multicollinearity before building land change models, making it possible to simulate more realistic outcomes.

  15. ReaDDy--a software for particle-based reaction-diffusion dynamics in crowded cellular environments.

    Directory of Open Access Journals (Sweden)

    Johannes Schöneberg

    Full Text Available We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics.

  16. Genetic Algorithm Calibration of Probabilistic Cellular Automata for Modeling Mining Permit Activity

    Science.gov (United States)

    Louis, S.J.; Raines, G.L.

    2003-01-01

    We use a genetic algorithm to calibrate a spatially and temporally resolved cellular automata to model mining activity on public land in Idaho and western Montana. The genetic algorithm searches through a space of transition rule parameters of a two dimensional cellular automata model to find rule parameters that fit observed mining activity data. Previous work by one of the authors in calibrating the cellular automaton took weeks - the genetic algorithm takes a day and produces rules leading to about the same (or better) fit to observed data. These preliminary results indicate that genetic algorithms are a viable tool in calibrating cellular automata for this application. Experience gained during the calibration of this cellular automata suggests that mineral resource information is a critical factor in the quality of the results. With automated calibration, further refinements of how the mineral-resource information is provided to the cellular automaton will probably improve our model.

  17. A Cellular Automaton / Finite Element model for predicting grain texture development in galvanized coatings

    Science.gov (United States)

    Guillemot, G.; Avettand-Fènoël, M.-N.; Iosta, A.; Foct, J.

    2011-01-01

    Hot-dipping galvanizing process is a widely used and efficient way to protect steel from corrosion. We propose to master the microstructure of zinc grains by investigating the relevant process parameters. In order to improve the texture of this coating, we model grain nucleation and growth processes and simulate the zinc solid phase development. A coupling scheme model has been applied with this aim. This model improves a previous two-dimensional model of the solidification process. It couples a cellular automaton (CA) approach and a finite element (FE) method. CA grid and FE mesh are superimposed on the same domain. The grain development is simulated at the micro-scale based on the CA grid. A nucleation law is defined using a Gaussian probability and a random set of nucleating cells. A crystallographic orientation is defined for each one with a choice of Euler's angle (Ψ,θ,φ). A small growing shape is then associated to each cell in the mushy domain and a dendrite tip kinetics is defined using the model of Kurz [2]. The six directions of basal plane and the two perpendicular directions develop in each mushy cell. During each time step, cell temperature and solid fraction are then determined at micro-scale using the enthalpy conservation relation and variations are reassigned at macro-scale. This coupling scheme model enables to simulate the three-dimensional growing kinetics of the zinc grain in a two-dimensional approach. Grain structure evolutions for various cooling times have been simulated. Final grain structure has been compared to EBSD measurements. We show that the preferentially growth of dendrite arms in the basal plane of zinc grains is correctly predicted. The described coupling scheme model could be applied for simulated other product or manufacturing processes. It constitutes an approach gathering both micro and macro scale models.

  18. Cellular Automata and the Humanities.

    Science.gov (United States)

    Gallo, Ernest

    1994-01-01

    The use of cellular automata to analyze several pre-Socratic hypotheses about the evolution of the physical world is discussed. These hypotheses combine characteristics of both rigorous and metaphoric language. Since the computer demands explicit instructions for each step in the evolution of the automaton, such models can reveal conceptual…

  19. FPGA Implementation of one-dimensional and two-dimensional cellular automata

    International Nuclear Information System (INIS)

    D'Antone, I.

    1999-01-01

    This report describes the hardware implementation of one-dimensional and two-dimensional cellular automata (CAs). After a general introduction to the cellular automata, we consider a one-dimensional CA used to implement pseudo-random techniques in built-in self test for VLSI. Due to the increase in digital ASIC complexity, testing is becoming one of the major costs in the VLSI production. The high electronics complexity, used in particle physics experiments, demands higher reliability than in the past time. General criterions are given to evaluate the feasibility of the circuit used for testing and some quantitative parameters are underlined to optimize the architecture of the cellular automaton. Furthermore, we propose a two-dimensional CA that performs a peak finding algorithm in a matrix of cells mapping a sub-region of a calorimeter. As in a two-dimensional filtering process, the peaks of the energy clusters are found in one evolution step. This CA belongs to Wolfram class II cellular automata. Some quantitative parameters are given to optimize the architecture of the cellular automaton implemented in a commercial field programmable gate array (FPGA)

  20. RKC time-stepping for advection-diffusion-reaction problems

    International Nuclear Information System (INIS)

    Verwer, J.G.; Sommeijer, B.P.; Hundsdorfer, W.

    2004-01-01

    The original explicit Runge-Kutta-Chebyshev (RKC) method is a stabilized second-order integration method for pure diffusion problems. Recently, it has been extended in an implicit-explicit manner to also incorporate highly stiff reaction terms. This implicit-explicit RKC method thus treats diffusion terms explicitly and the highly stiff reaction terms implicitly. The current paper deals with the incorporation of advection terms for the explicit method, thus aiming at the implicit-explicit RKC integration of advection-diffusion-reaction equations in a manner that advection and diffusion terms are treated simultaneously and explicitly and the highly stiff reaction terms implicitly

  1. Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model study.

    Science.gov (United States)

    Brandt-Pollmann, U; Lebiedz, D; Diehl, M; Sager, S; Schlöder, J

    2005-09-01

    Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.

  2. Inertial effects in diffusion-limited reactions

    International Nuclear Information System (INIS)

    Dorsaz, N; Foffi, G; De Michele, C; Piazza, F

    2010-01-01

    Diffusion-limited reactions are commonly found in biochemical processes such as enzyme catalysis, colloid and protein aggregation and binding between different macromolecules in cells. Usually, such reactions are modeled within the Smoluchowski framework by considering purely diffusive boundary problems. However, inertial effects are not always negligible in real biological or physical media on typical observation time frames. This is all the more so for non-bulk phenomena involving physical boundaries, that introduce additional time and space constraints. In this paper, we present and test a novel numerical scheme, based on event-driven Brownian dynamics, that allows us to explore a wide range of velocity relaxation times, from the purely diffusive case to the underdamped regime. We show that our algorithm perfectly reproduces the solution of the Fokker-Planck problem with absorbing boundary conditions in all the regimes considered and is thus a good tool for studying diffusion-guided reactions in complex biological environments.

  3. Reaction diffusion in chromium-zircaloy-2 system

    International Nuclear Information System (INIS)

    Xiang Wenxin; Ying Shihao

    2001-01-01

    Reaction diffusion in the chromium-zircaloy-2 diffusion couples is investigated in the temperature range of 1023 - 1123 K. Scanning electron microscope (SEM) and energy dispersive spectrum (EDS) were used to measure the thickness of the reaction layer and to determine the Zr, Fe and Cr concentration penetrate profile in reaction layer, respectively. The growth kinetics of reaction layer has been studied and the results show that the growth of intermetallic compound is controlled by the process of volume diffusion as the layer growth approximately obeys the parabolic law. Interdiffusion coefficients were calculated using Boltzmann-Matano-Heumann model. Calculated interdiffusion coefficients were compared with those obtained on the condition that Cr dissolves in Zr and merely forms dilute solid solution. The comparison indicates that Cr diffuses in dilute solid solution is five orders of magnitude faster than in Zr(Fe, Cr) 2 intermetallic compound

  4. Turing instability in reaction-diffusion systems with nonlinear diffusion

    Energy Technology Data Exchange (ETDEWEB)

    Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

    2013-10-15

    The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.

  5. Deterministic one-way simulation of two-way, real-time cellular automata and its related problems

    Energy Technology Data Exchange (ETDEWEB)

    Umeo, H; Morita, K; Sugata, K

    1982-06-13

    The authors show that for any deterministic two-way, real-time cellular automaton, m, there exists a deterministic one-way cellular automation which can simulate m in twice real-time. Moreover the authors present a new type of deterministic one-way cellular automata, called circular cellular automata, which are computationally equivalent to deterministic two-way cellular automata. 7 references.

  6. Overview of cellular automaton models for corrosion

    International Nuclear Information System (INIS)

    Perez-Brokate, Cristian Felipe; De Lamare, Jacques; Dung di Caprio; Feron, Damien; Chausse, Annie

    2014-01-01

    A review of corrosion process modeling using cellular automata methods is presented. This relatively new and growing approach takes into account the stochastic nature of the phenomena and uses physico-chemical rules to make predictions at a mesoscopic scale. Milestone models are analyzed and perspectives are established. (authors)

  7. A cellular automata approach to chemical reactions : 1 reaction controlled systems

    NARCIS (Netherlands)

    Korte, de A.C.J.; Brouwers, H.J.H.

    2013-01-01

    A direct link between the chemical reaction controlled (shrinking core) model and cellular automata, to study the dissolution of particles, is derived in this paper. Previous research on first and second order reactions is based on the concentration of the reactant. The present paper describes the

  8. A quantum Samaritan’s dilemma cellular automaton

    Science.gov (United States)

    Situ, Haozhen

    2017-01-01

    The dynamics of a spatial quantum formulation of the iterated Samaritan’s dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e. with local and synchronous interaction. The game is assessed in fair and unfair contests, in noiseless scenarios and with disrupting quantum noise. PMID:28680654

  9. Feynman-Kac equations for reaction and diffusion processes

    Science.gov (United States)

    Hou, Ru; Deng, Weihua

    2018-04-01

    This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

  10. Distributed order reaction-diffusion systems associated with Caputo derivatives

    Science.gov (United States)

    Saxena, R. K.; Mathai, A. M.; Haubold, H. J.

    2014-08-01

    This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. ["The fundamental solution of the space-time fractional diffusion equation," Fractional Calculus Appl. Anal. 4, 153-202 (2001); Mainardi et al. "Fox H-functions in fractional diffusion," J. Comput. Appl. Math. 178, 321-331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. ["Solutions of reaction-diffusion equations in terms of the H-function," Bull. Astron. Soc. India 35, 681-689 (2007)] and Saxena et al. ["Fractional reaction-diffusion equations," Astrophys. Space Sci. 305, 289-296 (2006a)] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion, see Schneider and Wyss ["Fractional diffusion and wave equations," J. Math. Phys. 30, 134-144 (1989)]. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables

  11. Quantum field theoretic behavior of a deterministic cellular automaton

    Energy Technology Data Exchange (ETDEWEB)

    Hooft, G ' t; Isler, K; Kalitzin, S [Inst. for Theoretical Physics, Utrecht (Netherlands)

    1992-11-16

    A certain class of cellular automata in 1 space +1 time dimension is shown to be closely related to quantum field theories containing Dirac fermions. In the massless case this relation can be studied analytically, while the introduction of Dirac mass requires numerical simulations. We show that in the last case the cellular automation describes the corresponding field theory only approximately. (orig.).

  12. Peculiarities of hardware implementation of generalized cellular tetra automaton

    OpenAIRE

    Аноприенко, Александр Яковлевич; Федоров, Евгений Евгениевич; Иваница, Сергей Васильевич; Альрабаба, Хамза

    2015-01-01

    Cellular automata are widely used in many fields of knowledge for the study of variety of complex real processes: computer engineering and computer science, cryptography, mathematics, physics, chemistry, ecology, biology, medicine, epidemiology, geology, architecture, sociology, theory of neural networks. Thus, cellular automata (CA) and tetra automata are gaining relevance taking into account the hardware and software solutions.Also it is marked a trend towards an increase in the number of p...

  13. Stochastic reaction-diffusion algorithms for macromolecular crowding

    Science.gov (United States)

    Sturrock, Marc

    2016-06-01

    Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.

  14. Algorithmic crystal chemistry: A cellular automata approach

    International Nuclear Information System (INIS)

    Krivovichev, S. V.

    2012-01-01

    Atomic-molecular mechanisms of crystal growth can be modeled based on crystallochemical information using cellular automata (a particular case of finite deterministic automata). In particular, the formation of heteropolyhedral layered complexes in uranyl selenates can be modeled applying a one-dimensional three-colored cellular automaton. The use of the theory of calculations (in particular, the theory of automata) in crystallography allows one to interpret crystal growth as a computational process (the realization of an algorithm or program with a finite number of steps).

  15. Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles

    Science.gov (United States)

    Szymańska, Paulina; Kochańczyk, Marek; Miekisz, Jacek; Lipniacki, Tomasz

    2015-02-01

    We investigate the kinetics of the ubiquitous phosphorylation-dephosphorylation cycle on biological membranes by means of kinetic Monte Carlo simulations on the triangular lattice. We establish the dependence of effective macroscopic reaction rate coefficients as well as the steady-state phosphorylated substrate fraction on the diffusion coefficient and concentrations of opposing enzymes: kinases and phosphatases. In the limits of zero and infinite diffusion, the numerical results agree with analytical predictions; these two limits give the lower and the upper bound for the macroscopic rate coefficients, respectively. In the zero-diffusion limit, which is important in the analysis of dense systems, phosphorylation and dephosphorylation reactions can convert only these substrates which remain in contact with opposing enzymes. In the most studied regime of nonzero but small diffusion, a contribution linearly proportional to the diffusion coefficient appears in the reaction rate. In this regime, the presence of opposing enzymes creates inhomogeneities in the (de)phosphorylated substrate distributions: The spatial correlation function shows that enzymes are surrounded by clouds of converted substrates. This effect becomes important at low enzyme concentrations, substantially lowering effective reaction rates. Effective reaction rates decrease with decreasing diffusion and this dependence is more pronounced for the less-abundant enzyme. Consequently, the steady-state fraction of phosphorylated substrates can increase or decrease with diffusion, depending on relative concentrations of both enzymes. Additionally, steady states are controlled by molecular crowders which, mostly by lowering the effective diffusion of reactants, favor the more abundant enzyme.

  16. Nonlinear analysis of a reaction-diffusion system: Amplitude equations

    Energy Technology Data Exchange (ETDEWEB)

    Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

    2012-10-15

    A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.

  17. Cellular-automata method for phase unwrapping

    International Nuclear Information System (INIS)

    Ghiglia, D.C.; Mastin, G.A.; Romero, L.A.

    1987-01-01

    Research into two-dimensional phase unwrapping has uncovered interesting and troublesome inconsistencies that cause path-dependent results. Cellular automata, which are simple, discrete mathematical systems, offered promise of computation in nondirectional, parallel manner. A cellular automaton was discovered that can unwrap consistent phase data in n dimensions in a path-independent manner and can automatically accommodate noise-induced (pointlike) inconsistencies and arbitrary boundary conditions (region partitioning). For data with regional (nonpointlike) inconsistencies, no phase-unwrapping algorithm will converge, including the cellular-automata approach. However, the automata method permits more simple visualization of the regional inconsistencies. Examples of its behavior on one- and two-dimensional data are presented

  18. Exact analytical solutions for nonlinear reaction-diffusion equations

    International Nuclear Information System (INIS)

    Liu Chunping

    2003-01-01

    By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way

  19. Speed ot travelling waves in reaction-diffusion equations

    International Nuclear Information System (INIS)

    Benguria, R.D.; Depassier, M.C.; Mendez, V.

    2002-01-01

    Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)

  20. Study of ODE limit problems for reaction-diffusion equations

    Directory of Open Access Journals (Sweden)

    Jacson Simsen

    2018-01-01

    Full Text Available In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in \\(L^{\\infty}(\\Omega\\ and the diffusion coefficients go to infinity.

  1. Field theory of propagating reaction-diffusion fronts

    International Nuclear Information System (INIS)

    Escudero, C.

    2004-01-01

    The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations

  2. Model checking of time Petri nets using the state class timed automaton

    DEFF Research Database (Denmark)

    Lime, Didier; Roux, Olivier H.

    2006-01-01

    In this paper, we propose a method for building the state class graph of a bounded time Petri net (TPN) as a timed automaton (TA), which we call the state class timed automaton. We consider bounded TPN, whose underlying net is not necessarily bounded. We prove that our translation preserves the b...

  3. Nonlinear variational models for reaction and diffusion systems

    International Nuclear Information System (INIS)

    Tanyi, G.E.

    1983-08-01

    There exists a natural metric w.r.t. which the density dependent diffusion operator is harmonic in the sense of Eells and Sampson. A physical corollary of this statement is the property that any two regular points on the orbit of a reaction or diffusion operator can be connected by a path along which the reaction rate is constant. (author)

  4. Diffusion limited reactions in crystalline solids

    International Nuclear Information System (INIS)

    Fastenau, R.

    1982-01-01

    Diffusion limited reactions in crystal lattices are studied with diffusion and random walk theory. First the random walk on a crystal lattice is studied. These results are used in a formal study of diffusion limited reactions in which the following simplified traps are discussed: planes, cylinders, spheres, disks and rings. The traps are either present at the start of the process (annealing) or fed into the crystal at a constant rate (continuous production). For the study of trapping processes occurring in real crystals it was necessary to investigate the interaction of the reacting species on the atomic level. Using lattice relaxation calculations, several reactions were studied. These calculations result in a model for the potential energy of the crystal versus the separation of the reaction partners. This model is used in Monte Carlo simulations of the trapping process, which are made at a high trap density, since the extrapolation to the low density regime can be made using the formal part of this work. The following reactions were studied: the trapping of interstitial helium atoms by vacancies, self interstitial vacancy recombination, the trapping of vacancies by immobile, helium filled, vacancies and the capture of self interstitials and vacancies by dislocations. A part of these results is used in two models for the low temperature nucleation and growth of bubbles due to helium bombardment. The models described give the right bubble density versus helium dose, but differ widely in the fraction of helium present in the bubbles found. A mechanism of blistering based on a percolation effect is also discussed. (Auth.)

  5. Reliable self-replicating machines in asynchronous cellular automata.

    Science.gov (United States)

    Lee, Jia; Adachi, Susumu; Peper, Ferdinand

    2007-01-01

    We propose a self-replicating machine that is embedded in a two-dimensional asynchronous cellular automaton with von Neumann neighborhood. The machine dynamically encodes its shape into description signals, and despite the randomness of cell updating, it is able to successfully construct copies of itself according to the description signals. Self-replication on asynchronously updated cellular automata may find application in nanocomputers, where reconfigurability is an essential property, since it allows avoidance of defective parts and simplifies programming of such computers.

  6. The Relationship between Cellular Phone Use, Performance, and Reaction Time among College Students: Implications for Cellular Phone Use while Driving

    Science.gov (United States)

    Szyfman, Adam; Wanner, Gregory; Spencer, Leslie

    2003-01-01

    Two studies were performed to determine the relationship between cellular phone use and either reaction time or performance among college students. In the first study 60 undergraduates completed a computerized reaction time test. Mean reaction times were significantly higher when participants were talking on a cellular phone, either handheld or on…

  7. Marine traffic model based on cellular automaton: Considering the change of the ship's velocity under the influence of the weather and sea

    Science.gov (United States)

    Qi, Le; Zheng, Zhongyi; Gang, Longhui

    2017-10-01

    It was found that the ships' velocity change, which is impacted by the weather and sea, e.g., wind, sea wave, sea current, tide, etc., is significant and must be considered in the marine traffic model. Therefore, a new marine traffic model based on cellular automaton (CA) was proposed in this paper. The characteristics of the ship's velocity change are taken into account in the model. First, the acceleration of a ship was divided into two components: regular component and random component. Second, the mathematical functions and statistical distribution parameters of the two components were confirmed by spectral analysis, curve fitting and auto-correlation analysis methods. Third, by combining the two components, the acceleration was regenerated in the update rules for ships' movement. To test the performance of the model, the ship traffic flows in the Dover Strait, the Changshan Channel and the Qiongzhou Strait were studied and simulated. The results show that the characteristics of ships' velocities in the simulations are consistent with the measured data by Automatic Identification System (AIS). Although the characteristics of the traffic flow in different areas are different, the velocities of ships can be simulated correctly. It proves that the velocities of ships under the influence of weather and sea can be simulated successfully using the proposed model.

  8. Instability induced by cross-diffusion in reaction-diffusion systems

    DEFF Research Database (Denmark)

    Tian, Canrong; Lin, Zhigui; Pedersen, Michael

    2010-01-01

    In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cros...... can induce the instability of an equilibrium which is stable for the kinetic system and for the self-diffusion–reaction system.......In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion...

  9. Ordering phase transition in the one-dimensional Axelrod model

    Science.gov (United States)

    Vilone, D.; Vespignani, A.; Castellano, C.

    2002-12-01

    We study the one-dimensional behavior of a cellular automaton aimed at the description of the formation and evolution of cultural domains. The model exhibits a non-equilibrium transition between a phase with all the system sharing the same culture and a disordered phase of coexisting regions with different cultural features. Depending on the initial distribution of the disorder the transition occurs at different values of the model parameters. This phenomenology is qualitatively captured by a mean-field approach, which maps the dynamics into a multi-species reaction-diffusion problem.

  10. Laser spot detection based on reaction diffusion

    Czech Academy of Sciences Publication Activity Database

    Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J. M.; Dormido, R.; Duro, N.

    2016-01-01

    Roč. 16, č. 3 (2016), s. 1-11, č. článku 315. ISSN 1424-8220 R&D Projects: GA MŠk EF15_008/0000162 Grant - others:ELI Beamlines(XE) CZ.02.1.01/0.0/0.0/15_008/0000162 Institutional support: RVO:68378271 Keywords : laser spot detection * laser beam detection * reaction diffusion models * Fitzhugh-Nagumo model * reaction diffusion computation * Turing patterns Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 2.677, year: 2016

  11. An extinction-survival-type phase transition in the probabilistic cellular automaton p182-q200

    International Nuclear Information System (INIS)

    Mendonca, J R G; Oliveira, M J de

    2011-01-01

    We investigate the critical behaviour of a probabilistic mixture of cellular automata (CA) rules 182 and 200 (in Wolfram's enumeration scheme) by mean-field analysis and Monte Carlo simulations. We found that as we switch off one CA and switch on the other by the variation of the single parameter of the model, the probabilistic CA (PCA) goes through an extinction-survival-type phase transition, and the numerical data indicate that it belongs to the directed percolation universality class of critical behaviour. The PCA displays a characteristic stationary density profile and a slow, diffusive dynamics close to the pure CA 200 point that we discuss briefly. Remarks on an interesting related stochastic lattice gas are addressed in the conclusions.

  12. Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

    Science.gov (United States)

    Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang

    2018-05-01

    Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

  13. A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation.

    Science.gov (United States)

    Arjunan, Satya Nanda Vel; Tomita, Masaru

    2010-03-01

    Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally. The online version of this article (doi:10.1007/s11693-009-9047-2) contains supplementary material, which is available to

  14. Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations

    KAUST Repository

    Alzahrani, Hasnaa H.

    2016-01-01

    A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge

  15. Correlation Between Minimum Apparent Diffusion Coefficient (ADCmin) and Tumor Cellularity: A Meta-analysis.

    Science.gov (United States)

    Surov, Alexey; Meyer, Hans Jonas; Wienke, Andreas

    2017-07-01

    Diffusion-weighted imaging (DWI) is a magnetic resonance imaging (MRI) technique based on measure of water diffusion that can provide information about tissue microstructure, especially about cell count. Increase of cell density induces restriction of water diffusion and decreases apparent diffusion coefficient (ADC). ADC can be divided into three sub-parameters: ADC minimum or ADC min , mean ADC or ADC mean and ADC maximum or ADC max Some studies have suggested that ADC min shows stronger correlations with cell count in comparison to other ADC fractions and may be used as a parameter for estimation of tumor cellularity. The aim of the present meta-analysis was to summarize correlation coefficients between ADC min and cellularity in different tumors based on large patient data. For this analysis, MEDLINE database was screened for associations between ADC and cell count in different tumors up to September 2016. For this work, only data regarding ADC min were included. Overall, 12 publications with 317 patients were identified. Spearman's correlation coefficient was used to analyze associations between ADC min and cellularity. The reported Pearson correlation coefficients in some publications were converted into Spearman correlation coefficients. The pooled correlation coefficient for all included studies was ρ=-0.59 (95% confidence interval (CI)=-0.72 to -0.45), heterogeneity Tau 2 =0.04 (pcorrelated moderately with tumor cellularity. The calculated correlation coefficient is not stronger in comparison to the reported coefficient for ADC mean and, therefore, ADC min does not represent a better means to reflect cellularity. Copyright© 2017, International Institute of Anticancer Research (Dr. George J. Delinasios), All rights reserved.

  16. Multi Car Elevator Control by using Learning Automaton

    Science.gov (United States)

    Shiraishi, Kazuaki; Hamagami, Tomoki; Hirata, Hironori

    We study an adaptive control technique for multi car elevators (MCEs) by adopting learning automatons (LAs.) The MCE is a high performance and a near-future elevator system with multi shafts and multi cars. A strong point of the system is that realizing a large carrying capacity in small shaft area. However, since the operation is too complicated, realizing an efficient MCE control is difficult for top-down approaches. For example, “bunching up together" is one of the typical phenomenon in a simple traffic environment like the MCE. Furthermore, an adapting to varying environment in configuration requirement is a serious issue in a real elevator service. In order to resolve these issues, having an autonomous behavior is required to the control system of each car in MCE system, so that the learning automaton, as the solutions for this requirement, is supposed to be appropriate for the simple traffic control. First, we assign a stochastic automaton (SA) to each car control system. Then, each SA varies its stochastic behavior distributions for adapting to environment in which its policy is evaluated with each passenger waiting times. That is LA which learns the environment autonomously. Using the LA based control technique, the MCE operation efficiency is evaluated through simulation experiments. Results show the technique enables reducing waiting times efficiently, and we confirm the system can adapt to the dynamic environment.

  17. Reversible one-dimensional cellular automata with one of the two Welch indices equal to 1 and full shifts

    International Nuclear Information System (INIS)

    Mora, Juan Carlos Seck Tuoh; Hernandez, Manuel Gonzalez; Vergara, Sergio V Chapa

    2003-01-01

    Reversible cellular automata are invertible discrete dynamical systems which have been widely studied both for analysing interesting theoretical questions and for obtaining relevant practical applications, for instance, simulating invertible natural systems or implementing data coding devices. An important problem in the theory of reversible automata is to know how the local behaviour which is not invertible is able to yield a reversible global one. In this sense, symbolic dynamics plays an important role for obtaining an adequate representation of a reversible cellular automaton. In this paper we prove the equivalence between a reversible automaton where the ancestors only differ at one side (technically with one of the two Welch indices equal to 1) and a full shift. We represent any reversible automaton by a de Bruijn diagram, and we characterize the way in which the diagram produces an evolution formed by undefined repetitions of two states. By means of amalgamations, we prove that there is always a way of transforming a de Bruijn diagram into the full shift. Finally, we provide an example illustrating the previous results

  18. Reversible one-dimensional cellular automata with one of the two Welch indices equal to 1 and full shifts

    Energy Technology Data Exchange (ETDEWEB)

    Mora, Juan Carlos Seck Tuoh [Centro de Investigacion Avanzada en Ingenieria Industrial, Universidad Autonoma del Estado de Hidalgo, Carr Pachuca-Tulancingo Km 4.5, 42020 Pachuca (Mexico); Hernandez, Manuel Gonzalez [Centro de Investigacion Avanzada en Ingenieria Industrial, Universidad Autonoma del Estado de Hidalgo, Carr Pachuca-Tulancingo Km 4.5, 42020 Pachuca (Mexico); Vergara, Sergio V Chapa [Depto de Ingenieria Electrica, Seccion Computacion, Centro de Investigacion y de Estudios Avanzados, Instituto Politecnico Nacional, Av IPN 2508, Col San Pedro Zacatenco, 07300 DF (Mexico)

    2003-07-25

    Reversible cellular automata are invertible discrete dynamical systems which have been widely studied both for analysing interesting theoretical questions and for obtaining relevant practical applications, for instance, simulating invertible natural systems or implementing data coding devices. An important problem in the theory of reversible automata is to know how the local behaviour which is not invertible is able to yield a reversible global one. In this sense, symbolic dynamics plays an important role for obtaining an adequate representation of a reversible cellular automaton. In this paper we prove the equivalence between a reversible automaton where the ancestors only differ at one side (technically with one of the two Welch indices equal to 1) and a full shift. We represent any reversible automaton by a de Bruijn diagram, and we characterize the way in which the diagram produces an evolution formed by undefined repetitions of two states. By means of amalgamations, we prove that there is always a way of transforming a de Bruijn diagram into the full shift. Finally, we provide an example illustrating the previous results.

  19. Restrictive liquid-phase diffusion and reaction in bidispersed catalysts

    International Nuclear Information System (INIS)

    Lee, S.Y.; Seader, J.D.; Tsai, C.H.; Massoth, F.E.

    1991-01-01

    In this paper, the effect of bidispersed pore-size distribution on liquid-phase diffusion and reaction in NiMo/Al 2 O 3 catalysts is investigated by applying two bidispersed-pore-structure models, the random-pore model and a globular-structure model, to extensive experimental data, which were obtained from sorptive diffusion measurements at ambient conditions and catalytic reaction rate measurements on nitrogen-containing compounds. Transport of the molecules in the catalysts was found to be controlled by micropore diffusion, in accordance with the random-pore model, rather than macropore diffusion as predicted by the globular-structure model. A qualitative criterion for micropore-diffusion control is proposed: relatively small macroporosity and high catalyst pellet density. Since most hydrotreating catalysts have high density, diffusion in these types of catalysts may be controlled by micropore diffusion. Accordingly, it is believed in this case that increasing the size of micropores may be more effective to reduce intraparticle diffusion resistance than incorporating macropores alone

  20. HEURISTIC METHOD FOR LOW POWER RACE-FREE STATE-ASSIGNMENT OF AN ASYNGHRONOUS AUTOMATON

    Directory of Open Access Journals (Sweden)

    Yu. V. Pottosin

    2016-01-01

    Full Text Available The problem of race free state-assignment of an asynchronous automaton minimizing the switching activity of memory elements in an implementing circuit is considered. A heuristic method to solve this problem for an asynchronous automaton is suggested where the critical races between memory elements of the implementing circuit are eliminated.

  1. Value of diffusion-Weighted imaging in evaluating the cellularity density of prostate cancer

    International Nuclear Information System (INIS)

    Liu Jingang; Wang Xizhen; Wang Bin; Niu Qingliang; Liu Qiang

    2008-01-01

    Objective: To study the cellularity density of prostate cancer (PCa) with diffusion-weighted imaging (DWI) and apparent diffusion coefficient (ADC). Methods: 38 patients with histologically proven prostate cancer (PCa) underwent DWI with a 1.5 T MR scanner using a pelvic phased array multi-coil. The ADC values of PCa, benign prostatic hyperplasia (BPH), and peripheral zone (PZ) were calculated. The cellularity density of PCa was recorded according to hematoxylin and eosin (HE) staining. The relationship between ADC value and cellularity density of PCa was analyzed with Pearson correlation coefficient. Results: The ADC values of PCa, BPH, and PZ were (49.32±12.68)×10 -5 mm 2 /s, (86.73±26.75)×10 -5 mm 2 /s and (126.25±27.21)×10 -5 mm 2 /s, respectively. The ADC value of PCa was significantly lower than that of BPH and PZ (P<005). The cellularity density of PCa was 12.9%. The ADC value reversely related to the cellularity density of prostate cancer (r=-0.646, P<005). Conclusion: The ADC value can reflect the cellularity density of PCa. (authors)

  2. Parametric spatiotemporal oscillation in reaction-diffusion systems.

    Science.gov (United States)

    Ghosh, Shyamolina; Ray, Deb Shankar

    2016-03-01

    We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.

  3. An extinction-survival-type phase transition in the probabilistic cellular automaton p182-q200

    Energy Technology Data Exchange (ETDEWEB)

    Mendonca, J R G; Oliveira, M J de, E-mail: jricardo@usp.br, E-mail: oliveira@if.usp.br [Instituto de Fisica, Universidade de Sao Paulo, Rua do Matao, Travessa R 187, Cidade Universitaria 05508-090, Sao Paulo (Brazil)

    2011-04-15

    We investigate the critical behaviour of a probabilistic mixture of cellular automata (CA) rules 182 and 200 (in Wolfram's enumeration scheme) by mean-field analysis and Monte Carlo simulations. We found that as we switch off one CA and switch on the other by the variation of the single parameter of the model, the probabilistic CA (PCA) goes through an extinction-survival-type phase transition, and the numerical data indicate that it belongs to the directed percolation universality class of critical behaviour. The PCA displays a characteristic stationary density profile and a slow, diffusive dynamics close to the pure CA 200 point that we discuss briefly. Remarks on an interesting related stochastic lattice gas are addressed in the conclusions.

  4. Splitting Schemes & Segregation In Reaction-(Cross-)Diffusion Systems

    OpenAIRE

    Carrillo, José A.; Fagioli, Simone; Santambrogio, Filippo; Schmidtchen, Markus

    2017-01-01

    One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction about their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to pr...

  5. Cellular reprogramming dynamics follow a simple 1D reaction coordinate

    Science.gov (United States)

    Teja Pusuluri, Sai; Lang, Alex H.; Mehta, Pankaj; Castillo, Horacio E.

    2018-01-01

    Cellular reprogramming, the conversion of one cell type to another, induces global changes in gene expression involving thousands of genes, and understanding how cells globally alter their gene expression profile during reprogramming is an ongoing problem. Here we reanalyze time-course data on cellular reprogramming from differentiated cell types to induced pluripotent stem cells (iPSCs) and show that gene expression dynamics during reprogramming follow a simple 1D reaction coordinate. This reaction coordinate is independent of both the time it takes to reach the iPSC state as well as the details of the experimental protocol used. Using Monte-Carlo simulations, we show that such a reaction coordinate emerges from epigenetic landscape models where cellular reprogramming is viewed as a ‘barrier-crossing’ process between cell fates. Overall, our analysis and model suggest that gene expression dynamics during reprogramming follow a canonical trajectory consistent with the idea of an ‘optimal path’ in gene expression space for reprogramming.

  6. Accurate numerical simulation of reaction-diffusion processes for heavy oil recovery

    Energy Technology Data Exchange (ETDEWEB)

    Govind, P.A.; Srinivasan, S. [Society of Petroleum Engineers, Richardson, TX (United States)]|[Texas Univ., Austin, TX (United States)

    2008-10-15

    This study evaluated a reaction-diffusion simulation tool designed to analyze the displacement of carbon dioxide (CO{sub 2}) in a simultaneous injection of carbon dioxide and elemental sodium in a heavy oil reservoir. Sodium was used due to the exothermic reaction of sodium with in situ that occurs when heat is used to reduce oil viscosity. The process also results in the formation of sodium hydroxide that reduces interfacial tension at the bitumen interface. A commercial simulation tool was used to model the sodium transport mechanism to the reaction interface through diffusion as well as the reaction zone's subsequent displacement. The aim of the study was to verify if the in situ reaction was able to generate sufficient heat to reduce oil viscosity and improve the displacement of the heavy oil. The study also assessed the accuracy of the reaction front simulation tool, in which an alternate method was used to model the propagation front as a moving heat source. The sensitivity of the simulation results were then evaluated in relation to the diffusion coefficient in order to understand the scaling characteristics of the reaction-diffusion zone. A pore-scale simulation was then up-scaled to grid blocks. Results of the study showed that when sodium suspended in liquid CO{sub 2} is injected into reservoirs, it diffuses through the carrier phase and interacts with water. A random walk diffusion algorithm with reactive dissipation was implemented to more accurately characterize reaction and diffusion processes. It was concluded that the algorithm modelled physical dispersion while neglecting the effect of numerical dispersion. 10 refs., 3 tabs., 24 figs.

  7. Cellular automata in photonic cavity arrays.

    Science.gov (United States)

    Li, Jing; Liew, T C H

    2016-10-31

    We propose theoretically a photonic Turing machine based on cellular automata in arrays of nonlinear cavities coupled with artificial gauge fields. The state of the system is recorded making use of the bistability of driven cavities, in which losses are fully compensated by an external continuous drive. The sequential update of the automaton layers is achieved automatically, by the local switching of bistable states, without requiring any additional synchronization or temporal control.

  8. Analytically solvable models of reaction-diffusion systems

    Energy Technology Data Exchange (ETDEWEB)

    Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)

    2004-05-01

    We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.

  9. Delay-induced wave instabilities in single-species reaction-diffusion systems

    Science.gov (United States)

    Otto, Andereas; Wang, Jian; Radons, Günter

    2017-11-01

    The Turing (wave) instability is only possible in reaction-diffusion systems with more than one (two) components. Motivated by the fact that a time delay increases the dimension of a system, we investigate the presence of diffusion-driven instabilities in single-species reaction-diffusion systems with delay. The stability of arbitrary one-component systems with a single discrete delay, with distributed delay, or with a variable delay is systematically analyzed. We show that a wave instability can appear from an equilibrium of single-species reaction-diffusion systems with fluctuating or distributed delay, which is not possible in similar systems with constant discrete delay or without delay. More precisely, we show by basic analytic arguments and by numerical simulations that fast asymmetric delay fluctuations or asymmetrically distributed delays can lead to wave instabilities in these systems. Examples, for the resulting traveling waves are shown for a Fisher-KPP equation with distributed delay in the reaction term. In addition, we have studied diffusion-induced instabilities from homogeneous periodic orbits in the same systems with variable delay, where the homogeneous periodic orbits are attracting resonant periodic solutions of the system without diffusion, i.e., periodic orbits of the Hutchinson equation with time-varying delay. If diffusion is introduced, standing waves can emerge whose temporal period is equal to the period of the variable delay.

  10. Decay to Equilibrium for Energy-Reaction-Diffusion Systems

    KAUST Repository

    Haskovec, Jan

    2018-02-06

    We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.

  11. Decay to Equilibrium for Energy-Reaction-Diffusion Systems

    KAUST Repository

    Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter A.; Mielke, Alexander

    2018-01-01

    We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.

  12. Analysis of diffusivity of the oscillating reaction components in a microreactor system

    Directory of Open Access Journals (Sweden)

    Martina Šafranko

    2017-01-01

    Full Text Available When performing oscillating reactions, periodical changes in the concentrations of reactants, intermediaries, and products take place. Due to the mentioned periodical changes of the concentrations, the information about the diffusivity of the components included into oscillating reactions is very important for the control of the oscillating reactions. Non-linear dynamics makes oscillating reactions very interesting for analysis in different reactor systems. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor, with the aim of identifying the limiting component. The geometry of the microreactor microchannel and a well defined flow profile ensure optimal conditions for the diffusion phenomena analysis, because diffusion profiles in a microreactor depend only on the residence time. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor equipped with 2 Y-shape inlets and 2 Y-shape outlets, with active volume of V = 4 μL at different residence times.

  13. Cellular automaton model of crowd evacuation inspired by slime mould

    Science.gov (United States)

    Kalogeiton, V. S.; Papadopoulos, D. P.; Georgilas, I. P.; Sirakoulis, G. Ch.; Adamatzky, A. I.

    2015-04-01

    In all the living organisms, the self-preservation behaviour is almost universal. Even the most simple of living organisms, like slime mould, is typically under intense selective pressure to evolve a response to ensure their evolution and safety in the best possible way. On the other hand, evacuation of a place can be easily characterized as one of the most stressful situations for the individuals taking part on it. Taking inspiration from the slime mould behaviour, we are introducing a computational bio-inspired model crowd evacuation model. Cellular Automata (CA) were selected as a fully parallel advanced computation tool able to mimic the Physarum's behaviour. In particular, the proposed CA model takes into account while mimicking the Physarum foraging process, the food diffusion, the organism's growth, the creation of tubes for each organism, the selection of optimum tube for each human in correspondence to the crowd evacuation under study and finally, the movement of all humans at each time step towards near exit. To test the model's efficiency and robustness, several simulation scenarios were proposed both in virtual and real-life indoor environments (namely, the first floor of office building B of the Department of Electrical and Computer Engineering of Democritus University of Thrace). The proposed model is further evaluated in a purely quantitative way by comparing the simulation results with the corresponding ones from the bibliography taken by real data. The examined fundamental diagrams of velocity-density and flow-density are found in full agreement with many of the already published corresponding results proving the adequacy, the fitness and the resulting dynamics of the model. Finally, several real Physarum experiments were conducted in an archetype of the aforementioned real-life environment proving at last that the proposed model succeeded in reproducing sufficiently the Physarum's recorded behaviour derived from observation of the aforementioned

  14. Image-Based Measurement of H2O2 Reaction-Diffusion in Wounded Zebrafish Larvae.

    Science.gov (United States)

    Jelcic, Mark; Enyedi, Balázs; Xavier, João B; Niethammer, Philipp

    2017-05-09

    Epithelial injury induces rapid recruitment of antimicrobial leukocytes to the wound site. In zebrafish larvae, activation of the epithelial NADPH oxidase Duox at the wound margin is required early during this response. Before injury, leukocytes are near the vascular region, that is, ∼100-300 μm away from the injury site. How Duox establishes long-range signaling to leukocytes is unclear. We conceived that extracellular hydrogen peroxide (H 2 O 2 ) generated by Duox diffuses through the tissue to directly regulate chemotactic signaling in these cells. But before it can oxidize cellular proteins, H 2 O 2 must get past the antioxidant barriers that protect the cellular proteome. To test whether, or on which length scales this occurs during physiological wound signaling, we developed a computational method based on reaction-diffusion principles that infers H 2 O 2 degradation rates from intravital H 2 O 2 -biosensor imaging data. Our results indicate that at high tissue H 2 O 2 levels the peroxiredoxin-thioredoxin antioxidant chain becomes overwhelmed, and H 2 O 2 degradation stalls or ceases. Although the wound H 2 O 2 gradient reaches deep into the tissue, it likely overcomes antioxidant barriers only within ∼30 μm of the wound margin. Thus, Duox-mediated long-range signaling may require other spatial relay mechanisms besides extracellular H 2 O 2 diffusion. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  15. Nonlinear reaction-diffusion systems conditional symmetry, exact solutions and their applications in biology

    CERN Document Server

    Cherniha, Roman

    2017-01-01

    This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems  and those developing the theoretical aspects of conditional symmetry conception,...

  16. Permanganate diffusion and reaction in sedimentary rocks.

    Science.gov (United States)

    Huang, Qiuyuan; Dong, Hailiang; Towne, Rachael M; Fischer, Timothy B; Schaefer, Charles E

    2014-04-01

    In situ chemical oxidation using permanganate has frequently been used to treat chlorinated solvents in fractured bedrock aquifers. However, in systems where matrix back-diffusion is an important process, the ability of the oxidant to migrate and treat target contaminants within the rock matrix will likely determine the overall effectiveness of this remedial approach. In this study, a series of diffusion experiments were performed to measure the permanganate diffusion and reaction in four different types of sedimentary rocks (dark gray mudstone, light gray mudstone, red sandstone, and tan sandstone). Results showed that, within the experimental time frame (~2 months), oxidant migration into the rock was limited to distances less than 500 μm. The observed diffusivities for permanganate into the rock matrices ranged from 5.3 × 10(-13) to 1.3 × 10(-11) cm(2)/s. These values were reasonably predicted by accounting for both the rock oxidant demand and the effective diffusivity of the rock. Various Mn minerals formed as surface coatings from reduction of permanganate coupled with oxidation of total organic carbon (TOC), and the nature of the formed Mn minerals was dependent upon the rock type. Post-treatment tracer testing showed that these Mn mineral coatings had a negligible impact on diffusion through the rock. Overall, our results showed that the extent of permanganate diffusion and reaction depended on rock properties, including porosity, mineralogy, and organic carbon. These results have important implications for our understanding of long-term organic contaminant remediation in sedimentary rocks using permanganate. Copyright © 2014 Elsevier B.V. All rights reserved.

  17. Chaotic advection, diffusion, and reactions in open flows

    International Nuclear Information System (INIS)

    Tel, Tamas; Karolyi, Gyoergy; Pentek, Aron; Scheuring, Istvan; Toroczkai, Zoltan; Grebogi, Celso; Kadtke, James

    2000-01-01

    We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity. (c) 2000 American Institute of Physics

  18. Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control.

    Science.gov (United States)

    Gan, Qintao; Lv, Tianshi; Fu, Zhenhua

    2016-04-01

    In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.

  19. External boundary effects on simultaneous diffusion and reaction processes

    International Nuclear Information System (INIS)

    Le Roux, M.N.; Wilhelmsson, H.

    1989-01-01

    External boundaries influence the spatial and temporal structure of evolution of dynamic systems governed by reaction-diffusion equations. Critical limits, i.e. thresholds for explosive growth or onset of diffusion dominated decay, are found to be caused by the presence of the boundary and to depend on: the position of the boundary, where the density is assumed to be zero at any instant of time: the mutual weights (coefficients) and powers of the nonlinear reaction and diffusion processes; and the initial spatial distribution. However, for particular relations between the nonlinear powers of the reaction and diffusion terms the critical limits do not depend on the initial conditions. The results are obtained by simulation experiment for one, two and three dimensions. Trends in the dynamic evolution of the system with an external boundary imposed are compared with the corresponding analytic results obtained for free boundary. Interesting applications are found in various areas, e.g. in the field of high temperature fusion plasma where the evolution of the temperature profile for the so-called H-mode (constant plasma density) is described

  20. Solutes and cells - aspects of advection-diffusion-reaction phenomena in biochips

    DEFF Research Database (Denmark)

    Vedel, Søren

    2012-01-01

    the dependencies on density. This shows that the varied single-cell behavior including the overall modulations imposed by density arise as a natural consequence of pseudopod-driven motility in a social context. The final subproject concerns the combined effects of advection, diffusion and reaction of several......Cell’), and the overall title of the project is Solutes and cells — aspects of advection-diffusion-reaction phenomena in biochips. The work has consisted of several projects focusing on theory, and to some extend analysis of experimental data, with advection-diffusion-reaction phenomena of solutes as the recurring theme...... quantitatively interpret the proximal concentration of specific solutes, and integrate this to achieve biological functions. In three specific examples, the author and co-workers have investigated different aspects of the influence of advection, diffusion and reaction on solute distributions, as well...

  1. 1D to 3D diffusion-reaction kinetics of defects in crystals

    DEFF Research Database (Denmark)

    Trinkaus, H.; Heinisch, H.L.; Barashev, A.V.

    2002-01-01

    Microstructural features evolving in crystalline solids from diffusion-reaction kinetics of mobile components depend crucially on the dimension of the underlying diffusion process which is commonly assumed to be three-dimensional (3D). In metals, irradiation-induced displacement cascades produce...... clusters of self-interstitials performing 1D diffusion. Changes between equivalent 1D diffusion paths and transversal diffusion result in diffusion-reaction kinetics between one and three dimensions. An analytical approach suggests a single-variable function (master curve) interpolating between the 1D...

  2. Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

    Energy Technology Data Exchange (ETDEWEB)

    Ho, C.-L. [Department of Physics, Tamkang University, Tamsui 25137, Taiwan (China); Lee, C.-C., E-mail: chieh.no27@gmail.com [Center of General Education, Aletheia University, Tamsui 25103, Taiwan (China)

    2016-01-15

    We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

  3. Numerical solution of a reaction-diffusion equation

    International Nuclear Information System (INIS)

    Moyano, Edgardo A.; Scarpettini, Alberto F.

    2000-01-01

    The purpose of the present work to continue the observations and the numerical experiences on a reaction-diffusion model, that is a simplified form of the neutronic flux equation. The model is parabolic, nonlinear, with Dirichlet boundary conditions. The purpose is to approximate non trivial solutions, asymptotically stables for t → ∞, that is solutions that tend to the elliptic problem, in the Lyapunov sense. It belongs to the so-called reaction-diffusion equations of semi linear kind, that is, linear equations in the heat operator and they have a nonlinear reaction function, in this case f (u, a, b) = u (a - b u), being u concentration, a and b parameters. The study of the incidence of these parameters take an interest to the neutronic flux physics. So that we search non trivial, positive and bounded solutions. The used algorithm is based on the concept of monotone and ordered sequences, and on the existence theorem of Amann and Sattinger. (author)

  4. Multidimensional cellular automata and generalization of Fekete's lemma

    Directory of Open Access Journals (Sweden)

    Silvio Capobianco

    2008-08-01

    Full Text Available Fekete's lemma is a well known combinatorial result on number sequences: we extend it to functions defined on $d$-tuples of integers. As an application of the new variant, we show that nonsurjective $d$-dimensional cellular automata are characterized by loss of arbitrarily much information on finite supports, at a growth rate greater than that of the support's boundary determined by the automaton's neighbourhood index.

  5. Bin packing problem solution through a deterministic weighted finite automaton

    Science.gov (United States)

    Zavala-Díaz, J. C.; Pérez-Ortega, J.; Martínez-Rebollar, A.; Almanza-Ortega, N. N.; Hidalgo-Reyes, M.

    2016-06-01

    In this article the solution of Bin Packing problem of one dimension through a weighted finite automaton is presented. Construction of the automaton and its application to solve three different instances, one synthetic data and two benchmarks are presented: N1C1W1_A.BPP belonging to data set Set_1; and BPP13.BPP belonging to hard28. The optimal solution of synthetic data is obtained. In the first benchmark the solution obtained is one more container than the ideal number of containers and in the second benchmark the solution is two more containers than the ideal solution (approximately 2.5%). The runtime in all three cases was less than one second.

  6. Investigation of the Practical Possibility of Solving Problems on Generalized Cellular Automata Associated with Cryptanalysis by Mean Algebraic Methods

    Directory of Open Access Journals (Sweden)

    P. G. Klyucharev

    2017-01-01

    Full Text Available A number of previous author’s papers proposed methods for constructing various cryptographic algorithms, including block ciphers and cryptographic hash functions, based on generalized cellular automata. This one is aimed at studying a possibility to use the algebraic cryptanalysis methods related to the construction of Gröbner bases for the generalized cellular automata to be applied in cryptography, i.e. this paper studies the possibility for using algebraic cryptanalysis methods to solve the problems of inversion of a generalized cellular automaton and recovering the key of such an automaton.If the cryptographic algorithm is represented as a system of polynomial equations over a certain finite field, then its breach is reduced to solving this system with respect to the key. Although the problem of solving a system of polynomial equations in a finite field is NP-difficult in the general case, the solution of a particular system can have low computational cost.Cryptanalysis based on the construction of a system of polynomial equations that links plain text, cipher-text and key, and its solution by algebraic methods, is usually called algebraic cryptanalysis. Among the main methods to solve systems of polynomial equations are those to construct Gröbner bases.Cryptanalysis of ciphers and hash functions based on generalized cellular automata can be reduced to various problems. We will consider two such problems: the problem of inversion of a generalized cellular automaton, which, in case we know the values of the cells after k iterations, enables us to find the initial values. And the task of recovering the key, which is to find the initial values of the remaining cells, using the cell values after k steps and the initial values of a part of the cells.A computational experiment was carried out to solve the two problems above stated in order to determine the maximum size of a generalized cellular automaton for which the solution of these

  7. Estimation and prediction of convection-diffusion-reaction systems from point measurement

    NARCIS (Netherlands)

    Vries, D.

    2008-01-01

    Different procedures with respect to estimation and prediction of systems characterized by convection, diffusion and reactions on the basis of point measurement data, have been studied. Two applications of these convection-diffusion-reaction (CDR) systems have been used as a case study of the

  8. A Cellular Automata-based Model for Simulating Restitution Property in a Single Heart Cell.

    Science.gov (United States)

    Sabzpoushan, Seyed Hojjat; Pourhasanzade, Fateme

    2011-01-01

    Ventricular fibrillation is the cause of the most sudden mortalities. Restitution is one of the specific properties of ventricular cell. The recent findings have clearly proved the correlation between the slope of restitution curve with ventricular fibrillation. This; therefore, mandates the modeling of cellular restitution to gain high importance. A cellular automaton is a powerful tool for simulating complex phenomena in a simple language. A cellular automaton is a lattice of cells where the behavior of each cell is determined by the behavior of its neighboring cells as well as the automata rule. In this paper, a simple model is depicted for the simulation of the property of restitution in a single cardiac cell using cellular automata. At first, two state variables; action potential and recovery are introduced in the automata model. In second, automata rule is determined and then recovery variable is defined in such a way so that the restitution is developed. In order to evaluate the proposed model, the generated restitution curve in our study is compared with the restitution curves from the experimental findings of valid sources. Our findings indicate that the presented model is not only capable of simulating restitution in cardiac cell, but also possesses the capability of regulating the restitution curve.

  9. Simulation of plant communities with a cellular automaton

    Energy Technology Data Exchange (ETDEWEB)

    Gassmann, F [Paul Scherrer Inst. (PSI), Villigen (Switzerland)

    1999-08-01

    With a modelling approach based on cellular automata, five observed types of plant development can be simulated. In addition, the proposed model shows a strong tendency towards the formation of patches and a high degree of dynamical and structural instability leading to limits of predictability for the asymptotic solution chosen by the system among several possible metastable patterns (multistability). Further, external fluctuations can be shown to have advantages for certain plant types. The presented model unifies the fundamental dichotomy in vegetation dynamics between determinism (understood as predictability) and disorder (chance effects) by showing the outcome of both classical theories as special cases. (author) 2 figs., 4 refs.

  10. Three-dimensional cellular automaton-finite element modeling of solidification grain structures for arc-welding processes

    International Nuclear Information System (INIS)

    Chen, Shijia; Guillemot, Gildas; Gandin, Charles-André

    2016-01-01

    Solidification grain structure has significant impact on the final properties of welded parts using fusion welding processes. Direct simulation of grain structure at industrial scale is yet rarely reported in the literature and remains a challenge. A three-dimensional (3D) coupled Cellular Automaton (CA) – Finite Element (FE) model is presented that predicts the grain structure formation during multiple passes Gas Tungsten Arc Welding (GTAW) and Gas Metal Arc Welding (GMAW). The FE model is established in a level set (LS) approach that tracks the evolution of the metal-shielding gas interface due to the addition of metal. The FE method solves the mass, energy and momentum conservation equations for the metal plus shielding gas system based on an adaptive mesh (FE mesh). Fields are projected in a second FE mesh, named CA mesh. A CA grid made of a regular lattice of cubic cells is created to overlay the fixed CA mesh. The CA model based on the CA grid simulates the melting and growth of the grain boundaries in the liquid pool. In order to handle large computational domains while keeping reasonable computational costs, parallel computations and dynamic strategies for the allocation/deallocation of the CA grid are introduced. These strategies correspond to significant optimizations of the computer memories that are demonstrated. The 3D CAFE model is first applied to the simple configuration of single linear passes by GTAW of a duplex stainless steel URANUS 2202. It is then applied to a more persuasive example considering GMAW in spray transfer mode during multiple passes to fill a V-groove chamfer. Simulations reveal the possibility to handle domains with millions of grains in representative domain sizes while following the formation of textures that result from the growth competition among columnar grains. -- Graphical abstract: Simulated 3D grain structure (3D CAFE model) for GTAW multiple linear passes at the surface of a duplex stainless steel (URANUS 22002

  11. Internal Diffusion-Controlled Enzyme Reaction: The Acetylcholinesterase Kinetics.

    Science.gov (United States)

    Lee, Sangyun; Kim, Ji-Hyun; Lee, Sangyoub

    2012-02-14

    Acetylcholinesterase is an enzyme with a very high turnover rate; it quenches the neurotransmitter, acetylcholine, at the synapse. We have investigated the kinetics of the enzyme reaction by calculating the diffusion rate of the substrate molecule along an active site channel inside the enzyme from atomic-level molecular dynamics simulations. In contrast to the previous works, we have found that the internal substrate diffusion is the determinant of the acetylcholinesterase kinetics in the low substrate concentration limit. Our estimate of the overall bimolecular reaction rate constant for the enzyme is in good agreement with the experimental data. In addition, the present calculation provides a reasonable explanation for the effects of the ionic strength of solution and the mutation of surface residues of the enzyme. The study suggests that internal diffusion of the substrate could be a key factor in understanding the kinetics of enzymes of similar characteristics.

  12. Turing Patterns in a Reaction-Diffusion System

    International Nuclear Information System (INIS)

    Wu Yanning; Wang Pingjian; Hou Chunju; Liu Changsong; Zhu Zhengang

    2006-01-01

    We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel-Epstein model. Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.

  13. Reaction-diffusion pulses: a combustion model

    International Nuclear Information System (INIS)

    Campos, Daniel; Llebot, Josep Enric; Fort, Joaquim

    2004-01-01

    We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations

  14. Reaction-diffusion pulses: a combustion model

    Energy Technology Data Exchange (ETDEWEB)

    Campos, Daniel [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Llebot, Josep Enric [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Fort, Joaquim [Dept. de FIsica, Univ. de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain)

    2004-07-02

    We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations.

  15. Cross-diffusional effect in a telegraph reaction diffusion Lotka-Volterra two competitive system

    International Nuclear Information System (INIS)

    Abdusalam, H.A; Fahmy, E.S.

    2003-01-01

    It is known now that, telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion in several branches of sciences. Telegraph reaction diffusion Lotka-Volterra two competitive system is considered. We observed that this system can give rise to diffusive instability only in the presence of cross-diffusion. Local and global stability analysis in the cross-diffusional effect are studied by considering suitable Lyapunov functional

  16. A study on the cellular stromal reaction and immunologic response of regional lymph nodes in gastric cancer

    International Nuclear Information System (INIS)

    Jyokoh, Hiroshi

    1986-01-01

    In an attempt to find a correlation between background factors and prognosis, cellular stromal reaction and PHA blastformation in the regional lymph nodes in gastric cancer were investigated in a total of 234 cases with advanced gastric cancer consisting of 104 patients who had undergone preoperative radiaiton therapy and 130 non-irradiated patients. The following results were obtained: 1) Interstitial matrix and fibrotic components around the gastric cancer cells proliferate. In addition, cellular components consisting mainly of lymphocytes appear in varied degrees. 2) In both non-irradiated and irradiated groups, there was no remarkable difference in the cellular stromal reaction among any major cancer sites. 3) In non-irradiated patients, no correlation existed between tumor diameters and cellular stromal reaction, while, in the irradiated cases, there were increases in the cellular stromal reaction where the tumor size is 5 cm or less. 4) In both non-irradiated and irradiated groups, cellular stromal reaction was more remarkable in highly differentiated carcinoma. 5) There were decreases in the cellular stromal reaction in ps(+) cases, of both non-irradiated and irradiated groups. 6) The cellular stromal reaction was remarkable in non-irradiated and irradiated patients who were found to be histologically negative in lymph node metastasis. 7) With the advance in staging, the cellular stromal reaction decreased in both irradiated and non-irradiated patients. 8) In both non-irradiated and irradiated groups, the cellular stromal reaction decreased in the patients who had shown vascular invasion. 9) PHA blastformation of the lymphocytes in lymph nodes of non-metastatic cases was more remarkable than that of metastatic cases, retaining high degrees of immunity. 10) In the non-metastatic patients in the lymph nodes outside the irradiated area, the lymphocytes in the lymph nodes demonstrated high degrees of PHA blastformation. (J.P.N.)

  17. Number-conserving cellular automata with a von Neumann neighborhood of range one

    International Nuclear Information System (INIS)

    Wolnik, Barbara; Dzedzej, Adam; Baetens, Jan M; De Baets, Bernard

    2017-01-01

    We present necessary and sufficient conditions for a cellular automaton with a von Neumann neighborhood of range one to be number-conserving. The conditions are formulated for any dimension and for any set of states containing zero. The use of the geometric structure of the von Neumann neighborhood allows for computationally tractable conditions even in higher dimensions. (paper)

  18. Liquid Film Diffusion on Reaction Rate in Submerged Biofilters

    DEFF Research Database (Denmark)

    Christiansen, Pia; Hollesen, Line; Harremoës, Poul

    1995-01-01

    Experiments were carried out in order to investigate the influence of liquid film diffusion on reaction rate in a submerged biofilter with denitrification and in order to compare with a theoretical study of the mass transfer coefficient. The experiments were carried out with varied flow, identified...... by the empty bed velocity of inflow and recirculation, respectively 1.3, 2.8, 5.6 and 10.9 m/h. The filter material consisted of 3 mm biostyren spheres. The results indicate that the influence of liquid film diffusion on reaction rate can be ignored....

  19. An adaptive algorithm for simulation of stochastic reaction-diffusion processes

    International Nuclear Information System (INIS)

    Ferm, Lars; Hellander, Andreas; Loetstedt, Per

    2010-01-01

    We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie's stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.

  20. A minimally-resolved immersed boundary model for reaction-diffusion problems

    OpenAIRE

    Pal Singh Bhalla, A; Griffith, BE; Patankar, NA; Donev, A

    2013-01-01

    We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blo...

  1. The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

    KAUST Repository

    Di Francesco, M.

    2008-12-08

    We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.

  2. Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

    2013-01-01

    In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

  3. Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion.

    Science.gov (United States)

    Zemskov, Evgeny P; Tsyganov, Mikhail A; Horsthemke, Werner

    2017-01-01

    We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system with linear cross diffusion. To be specific, we consider a piecewise linear approximation of the FitzHugh-Nagumo model, also known as the Bonhoeffer-van der Pol model. We focus on two types of traveling waves, namely solitary pulses that correspond to a homoclinic solution, and sequences of pulses or wave trains, i.e., a periodic solution. The effect of cross diffusion on wave profiles and speed of propagation is analyzed. We find the intriguing result that both pulses and wave trains occur in the bistable cross-diffusive FitzHugh-Nagumo system, whereas only fronts exist in the standard bistable system without cross diffusion.

  4. Multi-scale simulation of reaction-diffusion systems

    NARCIS (Netherlands)

    Vijaykumar, A.

    2017-01-01

    In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function

  5. Flow-Injection Responses of Diffusion Processes and Chemical Reactions

    DEFF Research Database (Denmark)

    Andersen, Jens Enevold Thaulov

    2000-01-01

    tool of automated analytical chemistry. The need for an even lower consumption of chemicals and for computer analysis has motivated a study of the FIA peak itself, that is, a theoretical model was developed, that provides detailed knowledge of the FIA profile. It was shown that the flow in a FIA...... manifold may be characterised by a diffusion coefficient that depends on flow rate, denoted as the kinematic diffusion coefficient. The description was applied to systems involving species of chromium, both in the case of simple diffusion and in the case of chemical reactions. It is suggested that it may...... be used in the resolution of FIA profiles to obtain information about the content of interference’s, in the study of chemical reaction kinetics and to measure absolute concentrations within the FIA-detector cell....

  6. An incomplete assembly with thresholding algorithm for systems of reaction-diffusion equations in three space dimensions IAT for reaction-diffusion systems

    International Nuclear Information System (INIS)

    Moore, Peter K.

    2003-01-01

    Solving systems of reaction-diffusion equations in three space dimensions can be prohibitively expensive both in terms of storage and CPU time. Herein, I present a new incomplete assembly procedure that is designed to reduce storage requirements. Incomplete assembly is analogous to incomplete factorization in that only a fixed number of nonzero entries are stored per row and a drop tolerance is used to discard small values. The algorithm is incorporated in a finite element method-of-lines code and tested on a set of reaction-diffusion systems. The effect of incomplete assembly on CPU time and storage and on the performance of the temporal integrator DASPK, algebraic solver GMRES and preconditioner ILUT is studied

  7. Computing aggregate properties of preimages for 2D cellular automata.

    Science.gov (United States)

    Beer, Randall D

    2017-11-01

    Computing properties of the set of precursors of a given configuration is a common problem underlying many important questions about cellular automata. Unfortunately, such computations quickly become intractable in dimension greater than one. This paper presents an algorithm-incremental aggregation-that can compute aggregate properties of the set of precursors exponentially faster than naïve approaches. The incremental aggregation algorithm is demonstrated on two problems from the two-dimensional binary Game of Life cellular automaton: precursor count distributions and higher-order mean field theory coefficients. In both cases, incremental aggregation allows us to obtain new results that were previously beyond reach.

  8. Intractable problems in reversible cellular automata

    International Nuclear Information System (INIS)

    Vatan, F.

    1988-01-01

    The billiard ball model, a classical mechanical system in which all parameters are real variables, can perform all digital computations. An eight-state, 11-neighbor reversible cellular automaton (an entirely discrete system in which all parameters are integer variables) can simulate this model. One of the natural problems for this system is to determine the shape of a container so that they initial specific distribution of gas molecules eventually leads to a predetermined distribution. This problem if PSPACE-complete. Related intractable and decidable problems are discussed as well

  9. Diffuse colonies of human skin fibroblasts in relation to cellular senescence and proliferation.

    Science.gov (United States)

    Zorin, Vadim; Zorina, Alla; Smetanina, Nadezhda; Kopnin, Pavel; Ozerov, Ivan V; Leonov, Sergey; Isaev, Artur; Klokov, Dmitry; Osipov, Andreyan N

    2017-05-16

    Development of personalized skin treatment in medicine and skin care may benefit from simple and accurate evaluation of the fraction of senescent skin fibroblasts that lost their proliferative capacity. We examined whether enriched analysis of colonies formed by primary human skin fibroblasts, a simple and widely available cellular assay, could reveal correlations with the fraction of senescent cells in heterogenic cell population. We measured fractions of senescence associated β-galactosidase (SA-βgal) positive cells in either mass cultures or colonies of various morphological types (dense, mixed and diffuse) formed by skin fibroblasts from 10 human donors. Although the donors were chosen to be within the same age group (33-54 years), the colony forming efficiency of their fibroblasts (ECO-f) and the percentage of dense, mixed and diffuse colonies varied greatly among the donors. We showed, for the first time, that the SA-βgal positive fraction was the largest in diffuse colonies, confirming that they originated from cells with the least proliferative capacity. The percentage of diffuse colonies was also found to correlate with the SA-βgal positive cells in mass culture. Using Ki67 as a cell proliferation marker, we further demonstrated a strong inverse correlation (r=-0.85, p=0.02) between the percentage of diffuse colonies and the fraction of Ki67+ cells. Moreover, a significant inverse correlation (r=-0.94, p=0.0001) between the percentage of diffuse colonies and ECO-f was found. Our data indicate that quantification of a fraction of diffuse colonies may provide a simple and useful method to evaluate the extent of cellular senescence in human skin fibroblasts.

  10. Reaction-diffusion controlled growth of complex structures

    Science.gov (United States)

    Noorduin, Willem; Mahadevan, L.; Aizenberg, Joanna

    2013-03-01

    Understanding how the emergence of complex forms and shapes in biominerals came about is both of fundamental and practical interest. Although biomineralization processes and organization strategies to give higher order architectures have been studied extensively, synthetic approaches to mimic these self-assembled structures are highly complex and have been difficult to emulate, let alone replicate. The emergence of solution patterns has been found in reaction-diffusion systems such as Turing patterns and the BZ reaction. Intrigued by this spontaneous formation of complexity we explored if similar processes can lead to patterns in the solid state. We here identify a reaction-diffusion system in which the shape of the solidified products is a direct readout of the environmental conditions. Based on insights in the underlying mechanism, we developed a toolbox of engineering strategies to deterministically sculpt patterns and shapes, and combine different morphologies to create a landscape of hierarchical multi scale-complex tectonic architectures with unprecedented levels of complexity. These findings may hold profound implications for understanding, mimicking and ultimately expanding upon nature's morphogenesis strategies, allowing the synthesis of advanced highly complex microscale materials and devices. WLN acknowledges the Netherlands Organization for Scientific Research for financial support

  11. Game of Life Cellular Automata

    CERN Document Server

    Adamatzky, Andrew

    2010-01-01

    In the late 1960s, British mathematician John Conway invented a virtual mathematical machine that operates on a two-dimensional array of square cell. Each cell takes two states, live and dead. The cells' states are updated simultaneously and in discrete time. A dead cell comes to life if it has exactly three live neighbours. A live cell remains alive if two or three of its neighbours are alive, otherwise the cell dies. Conway's Game of Life became the most programmed solitary game and the most known cellular automaton. The book brings together results of forty years of study into computational

  12. Contribution to an effective design method for stationary reaction-diffusion patterns

    International Nuclear Information System (INIS)

    Szalai, István; Horváth, Judit; De Kepper, Patrick

    2015-01-01

    The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences

  13. Contribution to an effective design method for stationary reaction-diffusion patterns

    Energy Technology Data Exchange (ETDEWEB)

    Szalai, István; Horváth, Judit [Laboratory of Nonlinear Chemical Dynamics, Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112 (Hungary); De Kepper, Patrick [Centre de Recherche Paul Pascal, CNRS, University of Bordeaux, 115, Avenue Schweitzer, F-33600 Pessac (France)

    2015-06-15

    The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.

  14. Exponential stability of delayed fuzzy cellular neural networks with diffusion

    International Nuclear Information System (INIS)

    Huang Tingwen

    2007-01-01

    The exponential stability of delayed fuzzy cellular neural networks (FCNN) with diffusion is investigated. Exponential stability, significant for applications of neural networks, is obtained under conditions that are easily verified by a new approach. Earlier results on the exponential stability of FCNN with time-dependent delay, a special case of the model studied in this paper, are improved without using the time-varying term condition: dτ(t)/dt < μ

  15. Application of neural networks and cellular automata to calorimetric problems

    International Nuclear Information System (INIS)

    Brenton, V.; Fonvieille, H.; Guicheney, C.; Jousset, J.; Roblin, Y.; Tamin, F.; Grenier, P.

    1994-09-01

    Computing techniques based on parallel processing have been used to treat the information from the electromagnetic calorimeters in SLAC experiments E142/E143. Cluster finding and separation of overlapping showers are performed by a cellular automaton, pion and electron identification is done by using a multilayered neural network. Both applications are presented and their resulting performances are shown to be improved compared to more standard approaches. (author)

  16. Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation

    Directory of Open Access Journals (Sweden)

    Petr Stehlík

    2015-01-01

    Full Text Available We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′  (or  Δtux=k(ux-1-2ux+ux+1+f(ux, x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.

  17. Wong-Zakai approximations and attractors for stochastic reaction-diffusion equations on unbounded domains

    Science.gov (United States)

    Wang, Xiaohu; Lu, Kening; Wang, Bixiang

    2018-01-01

    In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated long term behavior of the stochastic reaction-diffusion equation driven by a white noise. We first prove the existence and uniqueness of tempered pullback attractors for the Wong-Zakai approximations of stochastic reaction-diffusion equation. Then, we show that the attractors of Wong-Zakai approximations converges to the attractor of the stochastic reaction-diffusion equation for both additive and multiplicative noise.

  18. Invariant strings and pattern-recognizing properties of one-dimensional cellular automata

    International Nuclear Information System (INIS)

    Jen, E.

    1986-01-01

    A cellular automaton is a discrete dynamical system whose evolution is governed by a deterministic rule involving local interactions. It is shown that given an arbitrary string of values and an arbitry neighborhood size (representing the range of interaction), a simple procedure can be used to find the fules of that neighborhood size under which the string is unvarian. The set of nearestneighbor rules for which invariant strings exist is completely specified, as is the set of strings invariant under each such rule. For any automaton rule, an associated ''filtering'' rule is defined for which the only attractors are spatial sequences consisting of concatenations of invariant strings. A result is provided defining the rule of minimum neighborhood size for which an arbitrrily chosen string is the unique invariant string. The applications of filtering rules to pttern recognition problems are discussed

  19. Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.

    Science.gov (United States)

    Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young

    2017-03-14

    Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.

  20. Factorization, reduction and embedding in integrable cellular automata

    International Nuclear Information System (INIS)

    Kuniba, Atsuo; Takagi, Taichiro; Takenouchi, Akira

    2004-01-01

    Factorized dynamics in soliton cellular automata with quantum group symmetry is identified with a motion of particles and anti-particles exhibiting pair creation and annihilation. An embedding scheme is presented showing that the D (1) n -automaton contains, as certain subsectors, the box-ball systems and all the other automata associated with the crystal bases of non-exceptional affine Lie algebras. The results extend the earlier ones to higher representations by a certain reduction and to a wider class of boundary conditions

  1. Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

    Science.gov (United States)

    Yi, Taishan; Chen, Yuming

    2017-12-01

    In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

  2. Event-triggered synchronization for reaction-diffusion complex networks via random sampling

    Science.gov (United States)

    Dong, Tao; Wang, Aijuan; Zhu, Huiyun; Liao, Xiaofeng

    2018-04-01

    In this paper, the synchronization problem of the reaction-diffusion complex networks (RDCNs) with Dirichlet boundary conditions is considered, where the data is sampled randomly. An event-triggered controller based on the sampled data is proposed, which can reduce the number of controller and the communication load. Under this strategy, the synchronization problem of the diffusion complex network is equivalently converted to the stability of a of reaction-diffusion complex dynamical systems with time delay. By using the matrix inequality technique and Lyapunov method, the synchronization conditions of the RDCNs are derived, which are dependent on the diffusion term. Moreover, it is found the proposed control strategy can get rid of the Zeno behavior naturally. Finally, a numerical example is given to verify the obtained results.

  3. Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations

    KAUST Repository

    Alzahrani, Hasnaa H.

    2016-07-26

    A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.

  4. Modeling of the interplay between single-file diffusion and conversion reaction in mesoporous systems

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Jing [Iowa State Univ., Ames, IA (United States)

    2013-01-11

    We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. A strict single-file (no passing) constraint occurs in the diffusion within such narrow pores. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice–gas model for this reaction–diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction–diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction–diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion (SFD) in this multispecies system. Noting the shortcomings of mf-RDE and h-RDE, we then develop a generalized hydrodynamic (GH) formulation of appropriate gh-RDE which incorporates an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The gh-RDE elucidate the non-exponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth. Then an extended model of a catalytic conversion reaction within a functionalized nanoporous material is developed to assess the effect of varying the reaction product – pore interior interaction from attractive to repulsive. The analysis is performed utilizing the generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport for both irreversible and reversible reactions.

  5. Clarification of complex phenomena in nuclear plants present status and future trend of fluid analysis by cellular automaton methods

    International Nuclear Information System (INIS)

    Kato, Yasuyoshi

    1999-01-01

    Since most of complex phenomena comprise of various elementary processes e.g., fluid flow, heat conduction, phase transition, chemical reaction, structural deformation, and these processes interact each other nonlinearly, the complex phenomena cannot be easily clarified by such the conventional topdown approaches as describe phenomena by using differential equations. In contrast to the topdown approaches where the differential equations are located at the top of the analysis procedures, these are bottomup approaches where phenomena are reproduced by local interaction of particles on cells. Cellular automata are one of the typical bottomup approaches. The basic principle, computer simulation results, and massively parallel processors for the cellular automata are reviewed and perspectives of the bottomup approach are discussed on clarification of the complex phenomena in nuclear plants. The computer simulations mainly deal with fluid flows and phase interfacial phenomena. (author)

  6. Simulation of electrochemical processes in cardiac tissue based on cellular automaton

    International Nuclear Information System (INIS)

    Avdeev, S A; Bogatov, N M

    2014-01-01

    A new class of cellular automata using special accumulative function for nonuniformity distribution is presented. Usage of this automata type for simulation of excitable media applied to electrochemical processes in human cardiac tissue is shown

  7. Anomalous dimension in a two-species reaction-diffusion system

    Science.gov (United States)

    Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

    2018-01-01

    We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

  8. Reaction effects in diffusive shock acceleration

    International Nuclear Information System (INIS)

    Drury, L.Oc.

    1984-01-01

    The effects of the reaction of accelerated particles back on the shock wave in the diffusive-shock-acceleration model of cosmic-ray generation are investigated theoretically. Effects examined include changes in the shock structure, modifications of the input and output spectra, scattering effects, and possible instabilities in the small-scale structure. It is pointed out that the latter two effects are applicable to any spatially localized acceleration mechanism. 14 references

  9. A Weak Comparison Principle for Reaction-Diffusion Systems

    Directory of Open Access Journals (Sweden)

    José Valero

    2012-01-01

    Full Text Available We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L∞ is proved for at least one solution of the problem.

  10. Control of transversal instabilities in reaction-diffusion systems

    Science.gov (United States)

    Totz, Sonja; Löber, Jakob; Totz, Jan Frederik; Engel, Harald

    2018-05-01

    In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh–Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov–Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.

  11. Pattern formation in reaction diffusion systems with finite geometry

    International Nuclear Information System (INIS)

    Borzi, C.; Wio, H.

    1990-04-01

    We analyze the one-component, one-dimensional, reaction-diffusion equation through a simple inverse method. We confine the system and fix the boundary conditions as to induce pattern formation. We analyze the stability of those patterns. Our goal is to get information about the reaction term out of the preknowledgment of the pattern. (author). 5 refs

  12. Localizations in cellular automata with mutualistic excitation rules

    International Nuclear Information System (INIS)

    Adamatzky, Andrew

    2009-01-01

    Every cell of two-dimensional cellular automaton with eight-cell neighborhood takes three states: resting, excited and refractory, and updates excited to refractory and refractory to resting states unconditionally. A resting cell excites depending on number of excited and refractory neighbors. We made exhaustive study of spatio-temporal excitation dynamics for all rules of this type and selected several classes of rules. The classes supporting self-localizations are studied in details. We uncover basic types of mobile (gliders) and stationary localizations, and characterize their morphology and dynamics.

  13. A cellular automata model of Ebola virus dynamics

    Science.gov (United States)

    Burkhead, Emily; Hawkins, Jane

    2015-11-01

    We construct a stochastic cellular automaton (SCA) model for the spread of the Ebola virus (EBOV). We make substantial modifications to an existing SCA model used for HIV, introduced by others and studied by the authors. We give a rigorous analysis of the similarities between models due to the spread of virus and the typical immune response to it, and the differences which reflect the drastically different timing of the course of EBOV. We demonstrate output from the model and compare it with clinical data.

  14. Large-time behavior of solutions to a reaction-diffusion system with distributed microstructure

    NARCIS (Netherlands)

    Muntean, A.

    2009-01-01

    Abstract We study the large-time behavior of a class of reaction-diffusion systems with constant distributed microstructure arising when modeling diffusion and reaction in structured porous media. The main result of this Note is the following: As t ¿ 8 the macroscopic concentration vanishes, while

  15. Exact solutions of certain nonlinear chemotaxis diffusion reaction ...

    Indian Academy of Sciences (India)

    constructed coupled differential equations. The results obtained ... Nonlinear diffusion reaction equation; chemotaxis; auxiliary equation method; solitary wave solutions. ..... fact limits the scope of applications of the derived results. ... Research Fellowship and AP acknowledges DU and DST for PURSE grant for financial.

  16. Application of neural networks and cellular automata to calorimetric problems

    Energy Technology Data Exchange (ETDEWEB)

    Brenton, V; Fonvieille, H; Guicheney, C; Jousset, J; Roblin, Y; Tamin, F; Grenier, P

    1994-09-01

    Computing techniques based on parallel processing have been used to treat the information from the electromagnetic calorimeters in SLAC experiments E142/E143. Cluster finding and separation of overlapping showers are performed by a cellular automaton, pion and electron identification is done by using a multilayered neural network. Both applications are presented and their resulting performances are shown to be improved compared to more standard approaches. (author). 9 refs.; Submitted to Nuclear Instruments and Methods (NL).

  17. Reaction diffusion equations with boundary degeneracy

    Directory of Open Access Journals (Sweden)

    Huashui Zhan

    2016-03-01

    Full Text Available In this article, we consider the reaction diffusion equation $$ \\frac{\\partial u}{\\partial t} = \\Delta A(u,\\quad (x,t\\in \\Omega \\times (0,T, $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.

  18. Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays.

    Science.gov (United States)

    Sheng, Yin; Zhang, Hao; Zeng, Zhigang

    2017-10-01

    This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.

  19. Periodical cicadas: A minimal automaton model

    Science.gov (United States)

    de O. Cardozo, Giovano; de A. M. M. Silvestre, Daniel; Colato, Alexandre

    2007-08-01

    The Magicicada spp. life cycles with its prime periods and highly synchronized emergence have defied reasonable scientific explanation since its discovery. During the last decade several models and explanations for this phenomenon appeared in the literature along with a great deal of discussion. Despite this considerable effort, there is no final conclusion about this long standing biological problem. Here, we construct a minimal automaton model without predation/parasitism which reproduces some of these aspects. Our results point towards competition between different strains with limited dispersal threshold as the main factor leading to the emergence of prime numbered life cycles.

  20. Thermally activated reaction–diffusion-controlled chemical bulk reactions of gases and solids

    Directory of Open Access Journals (Sweden)

    S. Möller

    2015-01-01

    Full Text Available The chemical kinetics of the reaction of thin films with reactive gases is investigated. The removal of thin films using thermally activated solid–gas to gas reactions is a method to in-situ control deposition inventory in vacuum and plasma vessels. Significant scatter of experimental deposit removal rates at apparently similar conditions was observed in the past, highlighting the need for understanding the underlying processes. A model based on the presence of reactive gas in the films bulk and chemical kinetics is presented. The model describes the diffusion of reactive gas into the film and its chemical interaction with film constituents in the bulk using a stationary reaction–diffusion equation. This yields the reactive gas concentration and reaction rates. Diffusion and reaction rate limitations are depicted in parameter studies. Comparison with literature data on tokamak co-deposit removal results in good agreement of removal rates as a function of pressure, film thickness and temperature.

  1. Learning automaton newtork and its dynamics. Gakushu automaton network to sono dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Quan, F [Hiroshima-Denki Institute of Technology, Hiroshima (Jpaan); Unno, F; Hirata, H [Chiba Univ., Chiba (Japan)

    1991-10-20

    In order to construct a distributed processing system having learning automata as autonomous elements, a reinforcement learning network of the automaton is proposed and it{prime}s dynamics is investigated. In this paper, it is attempted to add another level of meaning to computational cooperativity by using a reinforcement learning network with generalized leaning automata. The collection of learning automata in the team situation acts as self-interested agents that work toward improving their performance with respect to their individual preference ordering. In the global state space of the network, the case of partially synchronous stochastic process is considered. In this case, the existence of mean field is shown and a reinforcement learning algorithm which can make the dynamics on the average reinforcement trajectory is presented. This algorithm is shown to have a high convergence speed as a result of a simple experiment. 14 refs., 9 figs.

  2. Cellular interface morphologies in directional solidification. III - The effects of heat transfer and solid diffusivity

    Science.gov (United States)

    Ungar, Lyle H.; Bennett, Mark J.; Brown, Robert A.

    1985-01-01

    The shape and stability of two-dimensional finite-amplitude cellular interfaces arising during directional solidification are compared for several solidification models that account differently for latent heat released at the interface, unequal thermal conductivities of melt and solid, and solute diffusivity in the solid. Finite-element analysis and computer-implemented perturbation methods are used to analyze the families of steadily growing cellular forms that evolve from the planar state. In all models a secondary bifurcation between different families of finite-amplitude cells exists that halves the spatial wavelength of the stable interface. The quantitative location of this transition is very dependent on the details of the model. Large amounts of solute diffusion in the solid retard the growth of large-amplitude cells.

  3. LOW POWER RACE-FREE STATE ASSIGNMENT OF AN ASYNGHRONOUS AUTOMATON

    Directory of Open Access Journals (Sweden)

    Yu. V. Pottosin

    2015-01-01

    Full Text Available The problem of a race free state assignment of an asynchronous automaton is considered. A method for the state assignment is suggested that provides the minimization of the number and theswitching activity of the memory elements along with the elimination of the critical races betweenthem.

  4. Variational methods applied to problems of diffusion and reaction

    CERN Document Server

    Strieder, William

    1973-01-01

    This monograph is an account of some problems involving diffusion or diffusion with simultaneous reaction that can be illuminated by the use of variational principles. It was written during a period that included sabbatical leaves of one of us (W. S. ) at the University of Minnesota and the other (R. A. ) at the University of Cambridge and we are grateful to the Petroleum Research Fund for helping to support the former and the Guggenheim Foundation for making possible the latter. We would also like to thank Stephen Prager for getting us together in the first place and for showing how interesting and useful these methods can be. We have also benefitted from correspondence with Dr. A. M. Arthurs of the University of York and from the counsel of Dr. B. D. Coleman the general editor of this series. Table of Contents Chapter 1. Introduction and Preliminaries . 1. 1. General Survey 1 1. 2. Phenomenological Descriptions of Diffusion and Reaction 2 1. 3. Correlation Functions for Random Suspensions 4 1. 4. Mean Free ...

  5. Distribution in flowing reaction-diffusion systems

    KAUST Repository

    Kamimura, Atsushi; Herrmann, Hans J.; Ito, Nobuyasu

    2009-01-01

    A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.

  6. Distribution in flowing reaction-diffusion systems

    KAUST Repository

    Kamimura, Atsushi

    2009-12-28

    A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.

  7. Toward an automaton Constraint for Local Search

    Directory of Open Access Journals (Sweden)

    Jun He

    2009-10-01

    Full Text Available We explore the idea of using finite automata to implement new constraints for local search (this is already a successful technique in constraint-based global search. We show how it is possible to maintain incrementally the violations of a constraint and its decision variables from an automaton that describes a ground checker for that constraint. We establish the practicality of our approach idea on real-life personnel rostering problems, and show that it is competitive with the approach of [Pralong, 2007].

  8. Hopf bifurcation in a delayed reaction-diffusion-advection population model

    Science.gov (United States)

    Chen, Shanshan; Lou, Yuan; Wei, Junjie

    2018-04-01

    In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.

  9. Solitary wave solutions of selective nonlinear diffusion-reaction ...

    Indian Academy of Sciences (India)

    An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlin- ear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences. Keywords.

  10. Rethinking pattern formation in reaction-diffusion systems

    Science.gov (United States)

    Halatek, J.; Frey, E.

    2018-05-01

    The present theoretical framework for the analysis of pattern formation in complex systems is mostly limited to the vicinity of fixed (global) equilibria. Here we present a new theoretical approach to characterize dynamical states arbitrarily far from (global) equilibrium. We show that reaction-diffusion systems that are driven by locally mass-conserving interactions can be understood in terms of local equilibria of diffusively coupled compartments. Diffusive coupling generically induces lateral redistribution of the globally conserved quantities, and the variable local amounts of these quantities determine the local equilibria in each compartment. We find that, even far from global equilibrium, the system is well characterized by its moving local equilibria. We apply this framework to in vitro Min protein pattern formation, a paradigmatic model for biological pattern formation. Within our framework we can predict and explain transitions between chemical turbulence and order arbitrarily far from global equilibrium. Our results reveal conceptually new principles of self-organized pattern formation that may well govern diverse dynamical systems.

  11. Endometrial cancer: correlation of apparent diffusion coefficient (ADC) with tumor cellularity and tumor grade.

    Science.gov (United States)

    Kishimoto, Keiko; Tajima, Shinya; Maeda, Ichiro; Takagi, Masayuki; Ueno, Takahiko; Suzuki, Nao; Nakajima, Yasuo

    2016-08-01

    Diffusion-weighted imaging (DWI) and the apparent diffusion coefficient (ADC) are widely used for detecting uterine endometrial cancer. The relationships between ADC values and pathological features of endometrial cancer have not yet been established. To investigate whether ADC values of endometrial cancer vary according to histologic tumor cellularity and tumor grade. We retrospectively reviewed 30 pathologically confirmed endometrial cancers. All patients underwent conventional non-enhanced magnetic resonance imaging (MRI) and DWI procedures, and ADC values were calculated. Tumor cellularity was evaluated by counting cancer cells in three high-power ( × 400) fields. The correlation between ADC values and tumor cellularity was assessed using Pearson's correlation coefficient test for statistical analysis. The mean ± standard deviation (SD) ADC value ( ×10(-3) mm(2)/s) of endometrial cancer was 0.85 ± 0.22 (range, 0.55-1.71). The mean ± SD tumor cellularity was 528.36 ± 16.89 (range, 298.0-763.6). ADC values were significantly inversely correlated with tumor cellularity. No significant relationship was observed between ADC values and tumor grade (mean ADC values: G1, 0.88 ± 0.265 × 10(-3) mm(2)/s; G2, 0.80 ± 0.178 × 10(-3) mm(2)/s; G3, 0.81 ± 0.117 × 10(-3) mm(2)/s). There is a significant inverse relationship between ADC values and tumor cellularity in endometrial cancer. No significant differences in average ADC value were observed between G1, G2, and G3 tumors. However, the lower the tumor grade, the wider the SD. © The Foundation Acta Radiologica 2015.

  12. One-electron oxidation reactions of purine and pyrimidine bases in cellular DNA.

    Science.gov (United States)

    Cadet, Jean; Wagner, J Richard; Shafirovich, Vladimir; Geacintov, Nicholas E

    2014-06-01

    The aim of this survey is to critically review the available information on one-electron oxidation reactions of nucleobases in cellular DNA with emphasis on damage induced through the transient generation of purine and pyrimidine radical cations. Since the indirect effect of ionizing radiation mediated by hydroxyl radical is predominant in cells, efforts have been made to selectively ionize bases using suitable one-electron oxidants that consist among others of high intensity UVC laser pulses. Thus, the main oxidation product in cellular DNA was found to be 8-oxo-7,8-dihydroguanine as a result of direct bi-photonic ionization of guanine bases and indirect formation of guanine radical cations through hole transfer reactions from other base radical cations. The formation of 8-oxo-7,8-dihydroguanine and other purine and pyrimidine degradation products was rationalized in terms of the initial generation of related radical cations followed by either hydration or deprotonation reactions in agreement with mechanistic pathways inferred from detailed mechanistic studies. The guanine radical cation has been shown to be implicated in three other nucleophilic additions that give rise to DNA-protein and DNA-DNA cross-links in model systems. Evidence was recently provided for the occurrence of these three reactions in cellular DNA. There is growing evidence that one-electron oxidation reactions of nucleobases whose mechanisms have been characterized in model studies involving aqueous solutions take place in a similar way in cells. It may also be pointed out that the above cross-linked lesions are only produced from the guanine radical cation and may be considered as diagnostic products of the direct effect of ionizing radiation.

  13. The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

    KAUST Repository

    Di Francesco, M.; Fellner, K.; Markowich, P. A

    2008-01-01

    and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid

  14. Modeling the potential spread of the recently identified non-native panther grouper (Chromileptes altivelis) in the Atlantic using a cellular automaton approach.

    Science.gov (United States)

    Johnston, Matthew W; Purkis, Sam J

    2013-01-01

    The Indo-pacific panther grouper (Chromileptes altiveli) is a predatory fish species and popular imported aquarium fish in the United States which has been recently documented residing in western Atlantic waters. To date, the most successful marine invasive species in the Atlantic is the lionfish (Pterois volitans/miles), which, as for the panther grouper, is assumed to have been introduced to the wild through aquarium releases. However, unlike lionfish, the panther grouper is not yet thought to have an established breeding population in the Atlantic. Using a proven modeling technique developed to track the lionfish invasion, presented is the first known estimation of the potential spread of panther grouper in the Atlantic. The employed cellular automaton-based computer model examines the life history of the subject species including fecundity, mortality, and reproductive potential and combines this with habitat preferences and physical oceanic parameters to forecast the distribution and periodicity of spread of this potential new invasive species. Simulations were examined for origination points within one degree of capture locations of panther grouper from the United States Geological Survey Nonindigenous Aquatic Species Database to eliminate introduction location bias, and two detailed case studies were scrutinized. The model indicates three primary locations where settlement is likely given the inputs and limits of the model; Jupiter Florida/Vero Beach, the Cape Hatteras Tropical Limit/Myrtle Beach South Carolina, and Florida Keys/Ten Thousand Islands locations. Of these locations, Jupiter Florida/Vero Beach has the highest settlement rate in the model and is indicated as the area in which the panther grouper is most likely to become established. This insight is valuable if attempts are to be made to halt this potential marine invasive species.

  15. Modeling the potential spread of the recently identified non-native panther grouper (Chromileptes altivelis in the Atlantic using a cellular automaton approach.

    Directory of Open Access Journals (Sweden)

    Matthew W Johnston

    Full Text Available The Indo-pacific panther grouper (Chromileptes altiveli is a predatory fish species and popular imported aquarium fish in the United States which has been recently documented residing in western Atlantic waters. To date, the most successful marine invasive species in the Atlantic is the lionfish (Pterois volitans/miles, which, as for the panther grouper, is assumed to have been introduced to the wild through aquarium releases. However, unlike lionfish, the panther grouper is not yet thought to have an established breeding population in the Atlantic. Using a proven modeling technique developed to track the lionfish invasion, presented is the first known estimation of the potential spread of panther grouper in the Atlantic. The employed cellular automaton-based computer model examines the life history of the subject species including fecundity, mortality, and reproductive potential and combines this with habitat preferences and physical oceanic parameters to forecast the distribution and periodicity of spread of this potential new invasive species. Simulations were examined for origination points within one degree of capture locations of panther grouper from the United States Geological Survey Nonindigenous Aquatic Species Database to eliminate introduction location bias, and two detailed case studies were scrutinized. The model indicates three primary locations where settlement is likely given the inputs and limits of the model; Jupiter Florida/Vero Beach, the Cape Hatteras Tropical Limit/Myrtle Beach South Carolina, and Florida Keys/Ten Thousand Islands locations. Of these locations, Jupiter Florida/Vero Beach has the highest settlement rate in the model and is indicated as the area in which the panther grouper is most likely to become established. This insight is valuable if attempts are to be made to halt this potential marine invasive species.

  16. Explosive instabilities of reaction-diffusion equations including pinch effects

    International Nuclear Information System (INIS)

    Wilhelmsson, H.

    1992-01-01

    Particular solutions of reaction-diffusion equations for temperature are obtained for explosively unstable situations. As a result of the interplay between inertial, diffusion, pinch and source processes certain 'bell-shaped' distributions may grow explosively in time with preserved shape of the spatial distribution. The effect of the pinch, which requires a density inhomogeneity, is found to diminish the effect of diffusion, or inversely to support the inertial and source processes in creating the explosion. The results may be described in terms of elliptic integrals or. more simply, by means of expansions in the spatial coordinate. An application is the temperature evolution of a burning fusion plasma. (au) (18 refs.)

  17. Cellular automata in image processing and geometry

    CERN Document Server

    Adamatzky, Andrew; Sun, Xianfang

    2014-01-01

    The book presents findings, views and ideas on what exact problems of image processing, pattern recognition and generation can be efficiently solved by cellular automata architectures. This volume provides a convenient collection in this area, in which publications are otherwise widely scattered throughout the literature. The topics covered include image compression and resizing; skeletonization, erosion and dilation; convex hull computation, edge detection and segmentation; forgery detection and content based retrieval; and pattern generation. The book advances the theory of image processing, pattern recognition and generation as well as the design of efficient algorithms and hardware for parallel image processing and analysis. It is aimed at computer scientists, software programmers, electronic engineers, mathematicians and physicists, and at everyone who studies or develops cellular automaton algorithms and tools for image processing and analysis, or develops novel architectures and implementations of mass...

  18. Effects on nuclear fusion reaction on diffusion and thermal conduction in a magnetoplasma

    International Nuclear Information System (INIS)

    Sakai, Kazuo; Aono, Osamu.

    1976-12-01

    In spite of the well spread belief in the field of irreversible thermodynamics, vectorial phenomena couple thermodynamically with the scalar phenomena. Transport coefficients concerning the diffusion and the thermal conduction across a strong magnetic field are calculated in the presence of the deuteron-triton fusion reaction on the basis of the gas kinetic theory. When the reaction takes place, the diffusion increases and the thermal conduction decreases. Effects of the reaction exceed those of the Coulomb collision as the temperature is high enough. (auth.)

  19. Dichotomous-noise-induced pattern formation in a reaction-diffusion system

    Science.gov (United States)

    Das, Debojyoti; Ray, Deb Shankar

    2013-06-01

    We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR) -membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.

  20. Exact solutions of some coupled nonlinear diffusion-reaction ...

    Indian Academy of Sciences (India)

    certain coupled diffusion-reaction (D-R) equations of very general nature. In recent years, various direct methods have been proposed to find the exact solu- tions not only of nonlinear partial differential equations but also of their coupled versions. These methods include unified ansatz approach [3], extended hyperbolic func ...

  1. Modelling non-homogeneous stochastic reaction-diffusion systems: the case study of gemcitabine-treated non-small cell lung cancer growth.

    Science.gov (United States)

    Lecca, Paola; Morpurgo, Daniele

    2012-01-01

    Reaction-diffusion based models have been widely used in the literature for modeling the growth of solid tumors. Many of the current models treat both diffusion/consumption of nutrients and cell proliferation. The majority of these models use classical transport/mass conservation equations for describing the distribution of molecular species in tumor spheroids, and the Fick's law for describing the flux of uncharged molecules (i.e oxygen, glucose). Commonly, the equations for the cell movement and proliferation are first order differential equations describing the rate of change of the velocity of the cells with respect to the spatial coordinates as a function of the nutrient's gradient. Several modifications of these equations have been developed in the last decade to explicitly indicate that the tumor includes cells, interstitial fluids and extracellular matrix: these variants provided a model of tumor as a multiphase material with these as the different phases. Most of the current reaction-diffusion tumor models are deterministic and do not model the diffusion as a local state-dependent process in a non-homogeneous medium at the micro- and meso-scale of the intra- and inter-cellular processes, respectively. Furthermore, a stochastic reaction-diffusion model in which diffusive transport of the molecular species of nutrients and chemotherapy drugs as well as the interactions of the tumor cells with these species is a novel approach. The application of this approach to he scase of non-small cell lung cancer treated with gemcitabine is also novel. We present a stochastic reaction-diffusion model of non-small cell lung cancer growth in the specification formalism of the tool Redi, we recently developed for simulating reaction-diffusion systems. We also describe how a spatial gradient of nutrients and oncological drugs affects the tumor progression. Our model is based on a generalization of the Fick's first diffusion law that allows to model diffusive transport in non

  2. Facilitating arrhythmia simulation: the method of quantitative cellular automata modeling and parallel running

    Directory of Open Access Journals (Sweden)

    Mondry Adrian

    2004-08-01

    Full Text Available Abstract Background Many arrhythmias are triggered by abnormal electrical activity at the ionic channel and cell level, and then evolve spatio-temporally within the heart. To understand arrhythmias better and to diagnose them more precisely by their ECG waveforms, a whole-heart model is required to explore the association between the massively parallel activities at the channel/cell level and the integrative electrophysiological phenomena at organ level. Methods We have developed a method to build large-scale electrophysiological models by using extended cellular automata, and to run such models on a cluster of shared memory machines. We describe here the method, including the extension of a language-based cellular automaton to implement quantitative computing, the building of a whole-heart model with Visible Human Project data, the parallelization of the model on a cluster of shared memory computers with OpenMP and MPI hybrid programming, and a simulation algorithm that links cellular activity with the ECG. Results We demonstrate that electrical activities at channel, cell, and organ levels can be traced and captured conveniently in our extended cellular automaton system. Examples of some ECG waveforms simulated with a 2-D slice are given to support the ECG simulation algorithm. A performance evaluation of the 3-D model on a four-node cluster is also given. Conclusions Quantitative multicellular modeling with extended cellular automata is a highly efficient and widely applicable method to weave experimental data at different levels into computational models. This process can be used to investigate complex and collective biological activities that can be described neither by their governing differentiation equations nor by discrete parallel computation. Transparent cluster computing is a convenient and effective method to make time-consuming simulation feasible. Arrhythmias, as a typical case, can be effectively simulated with the methods

  3. Heat Diffusion in Gases, Including Effects of Chemical Reaction

    Science.gov (United States)

    Hansen, C. Frederick

    1960-01-01

    The diffusion of heat through gases is treated where the coefficients of thermal conductivity and diffusivity are functions of temperature. The diffusivity is taken proportional to the integral of thermal conductivity, where the gas is ideal, and is considered constant over the temperature interval in which a chemical reaction occurs. The heat diffusion equation is then solved numerically for a semi-infinite gas medium with constant initial and boundary conditions. These solutions are in a dimensionless form applicable to gases in general, and they are used, along with measured shock velocity and heat flux through a shock reflecting surface, to evaluate the integral of thermal conductivity for air up to 5000 degrees Kelvin. This integral has the properties of a heat flux potential and replaces temperature as the dependent variable for problems of heat diffusion in media with variable coefficients. Examples are given in which the heat flux at the stagnation region of blunt hypersonic bodies is expressed in terms of this potential.

  4. The nature of turbulence in a triangular lattice gas automaton

    Science.gov (United States)

    Duong-Van, Minh; Feit, M. D.; Keller, P.; Pound, M.

    1986-12-01

    Power spectra calculated from the coarse-graining of a simple lattice gas automaton, and those of time averaging other stochastic times series that we have investigated, have exponents in the range -1.6 to -2, consistent with observation of fully developed turbulence. This power spectrum is a natural consequence of coarse-graining; the exponent -2 represents the continuum limit.

  5. Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

    Science.gov (United States)

    Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

    2011-03-21

    We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

  6. Calibrating cellular automaton models for pedestrians walking through corners

    Science.gov (United States)

    Dias, Charitha; Lovreglio, Ruggiero

    2018-05-01

    Cellular Automata (CA) based pedestrian simulation models have gained remarkable popularity as they are simpler and easier to implement compared to other microscopic modeling approaches. However, incorporating traditional floor field representations in CA models to simulate pedestrian corner navigation behavior could result in unrealistic behaviors. Even though several previous studies have attempted to enhance CA models to realistically simulate pedestrian maneuvers around bends, such modifications have not been calibrated or validated against empirical data. In this study, two static floor field (SFF) representations, namely 'discrete representation' and 'continuous representation', are calibrated for CA-models to represent pedestrians' walking behavior around 90° bends. Trajectory data collected through a controlled experiment are used to calibrate these model representations. Calibration results indicate that although both floor field representations can represent pedestrians' corner navigation behavior, the 'continuous' representation fits the data better. Output of this study could be beneficial for enhancing the reliability of existing CA-based models by representing pedestrians' corner navigation behaviors more realistically.

  7. Effect of Temperature and Fluid Flow on Dendrite Growth During Solidification of Al-3 Wt Pct Cu Alloy by the Two-Dimensional Cellular Automaton Method

    Science.gov (United States)

    Gu, Cheng; Wei, Yanhong; Liu, Renpei; Yu, Fengyi

    2017-12-01

    A two-dimensional cellular automaton-finite volume model was developed to simulate dendrite growth of Al-3 wt pct Cu alloy during solidification to investigate the effect of temperature and fluid flow on dendrite morphology, solute concentration distribution, and dendrite growth velocity. Different calculation conditions that may influence the results of the simulation, including temperature and flow, were considered. The model was also employed to study the effect of different undercoolings, applied temperature fields, and forced flow velocities on solute segregation and dendrite growth. The initial temperature and fluid flow have a significant impact on the dendrite morphologies and solute profiles during solidification. The release of energy is operated with solidification and results in the increase of temperature. A larger undercooling leads to larger solute concentration near the solid/liquid interface and solute concentration gradient at the same time-step. Solute concentration in the solid region tends to increase with the increase of undercooling. Four vortexes appear under the condition when natural flow exists: the two on the right of the dendrite rotate clockwise, and those on the left of the dendrite rotate counterclockwise. With the increase of forced flow velocity, the rejected solute in the upstream region becomes easier to be washed away and enriched in the downstream region, resulting in acceleration of the growth of the dendrite in the upstream and inhibiting the downstream dendrite growth. The dendrite perpendicular to fluid flow shows a coarser morphology in the upstream region than that of the downstream. Almost no secondary dendrite appears during the calculation process.

  8. Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

    KAUST Repository

    Madzvamuse, Anotida; Gaffney, Eamonn A.; Maini, Philip K.

    2009-01-01

    By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.

  9. Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

    KAUST Repository

    Madzvamuse, Anotida

    2009-08-29

    By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.

  10. Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays

    International Nuclear Information System (INIS)

    Liang Jinling; Cao Jinde

    2003-01-01

    Employing general Halanay inequality, we analyze the global exponential stability of a class of reaction-diffusion recurrent neural networks with time-varying delays. Several new sufficient conditions are obtained to ensure existence, uniqueness and global exponential stability of the equilibrium point of delayed reaction-diffusion recurrent neural networks. The results extend and improve the earlier publications. In addition, an example is given to show the effectiveness of the obtained result

  11. The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata

    International Nuclear Information System (INIS)

    Enrico Fermi, Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa (Italy))" data-affiliation=" (Dipartimento di Fisica Enrico Fermi, Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa (Italy))" >Elze, Hans-Thomas

    2014-01-01

    We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped reversibly on continuum equations describing a set of bandwidth limited harmonic oscillators. They represent the Schrödinger equation. However, modifications reflecting the bandwidth limit are incorporated, i.e., the presence of a time (or length) scale. When this discreteness scale is taken to zero, the usual results are obtained. Thus, the linearity of quantum mechanics can be traced to the postulated action principle of such cellular automata and its conservation laws to discrete ones. The cellular automaton conservation laws are in one-to-one correspondence with those of the related quantum mechanical model, while admissible symmetries are not.

  12. Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions

    International Nuclear Information System (INIS)

    Lu Junguo

    2008-01-01

    In this paper, the global exponential stability and periodicity for a class of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions are addressed by constructing suitable Lyapunov functionals and utilizing some inequality techniques. We first prove global exponential converge to 0 of the difference between any two solutions of the original reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions, the existence and uniqueness of equilibrium is the direct results of this procedure. This approach is different from the usually used one where the existence, uniqueness of equilibrium and stability are proved in two separate steps. Furthermore, we prove periodicity of the reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Sufficient conditions ensuring the global exponential stability and the existence of periodic oscillatory solutions for the reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions are given. These conditions are easy to check and have important leading significance in the design and application of reaction-diffusion recurrent neural networks with delays. Finally, two numerical examples are given to show the effectiveness of the obtained results

  13. FACC: A Novel Finite Automaton Based on Cloud Computing for the Multiple Longest Common Subsequences Search

    Directory of Open Access Journals (Sweden)

    Yanni Li

    2012-01-01

    Full Text Available Searching for the multiple longest common subsequences (MLCS has significant applications in the areas of bioinformatics, information processing, and data mining, and so forth, Although a few parallel MLCS algorithms have been proposed, the efficiency and effectiveness of the algorithms are not satisfactory with the increasing complexity and size of biologic data. To overcome the shortcomings of the existing MLCS algorithms, and considering that MapReduce parallel framework of cloud computing being a promising technology for cost-effective high performance parallel computing, a novel finite automaton (FA based on cloud computing called FACC is proposed under MapReduce parallel framework, so as to exploit a more efficient and effective general parallel MLCS algorithm. FACC adopts the ideas of matched pairs and finite automaton by preprocessing sequences, constructing successor tables, and common subsequences finite automaton to search for MLCS. Simulation experiments on a set of benchmarks from both real DNA and amino acid sequences have been conducted and the results show that the proposed FACC algorithm outperforms the current leading parallel MLCS algorithm FAST-MLCS.

  14. A numerical study of one-dimensional replicating patterns in reaction-diffusion systems with non-linear diffusion coefficients

    International Nuclear Information System (INIS)

    Ferreri, J. C.; Carmen, A. del

    1998-01-01

    A numerical study of the dynamics of pattern evolution in reaction-diffusion systems is performed, although limited to one spatial dimension. The diffusion coefficients are nonlinear, based on powers of the scalar variables. The system keeps the dynamics of previous studies in the literature, but the presence of nonlinear diffusion generates a field of strong nonlinear interactions due to the presence of receding travelling waves. This field is limited by the plane of symmetry of the space domain and the last born outgoing travelling wave. These effects are discussed. (author). 10 refs., 7 figs

  15. Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

    Science.gov (United States)

    Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

    2018-01-01

    This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

  16. Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

    Science.gov (United States)

    Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

    2018-06-01

    This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

  17. Reaction-diffusion modeling of hydrogen in beryllium

    Energy Technology Data Exchange (ETDEWEB)

    Wensing, Mirko; Matveev, Dmitry; Linsmeier, Christian [Forschungszentrum Juelich GmbH, Institut fuer Energie- und Klimaforschung - Plasmaphysik (Germany)

    2016-07-01

    Beryllium will be used as first-wall material for the future fusion reactor ITER as well as in the breeding blanket of DEMO. In both cases it is important to understand the mechanisms of hydrogen retention in beryllium. In earlier experiments with beryllium low-energy binding states of hydrogen were observed by thermal desorption spectroscopy (TDS) which are not yet well understood. Two candidates for these states are considered: beryllium-hydride phases within the bulk and surface effects. The retention of deuterium in beryllium is studied by a reaction rate approach using a coupled reaction diffusion system (CRDS)-model relying on ab initio data from density functional theory calculations (DFT). In this contribution we try to assess the influence of surface recombination.

  18. The correlation between apparent diffusion coefficient and tumor cellularity in patients: a meta-analysis.

    Science.gov (United States)

    Chen, Lihua; Liu, Min; Bao, Jing; Xia, Yunbao; Zhang, Jiuquan; Zhang, Lin; Huang, Xuequan; Wang, Jian

    2013-01-01

    To perform a meta-analysis exploring the correlation between the apparent diffusion coefficient (ADC) and tumor cellularity in patients. We searched medical and scientific literature databases for studies discussing the correlation between the ADC and tumor cellularity in patients. Only studies that were published in English or Chinese prior to November 2012 were considered for inclusion. Summary correlation coefficient (r) values were extracted from each study, and 95% confidence intervals (CIs) were calculated. Sensitivity and subgroup analyses were performed to investigate potential heterogeneity. Of 189 studies, 28 were included in the meta-analysis, comprising 729 patients. The pooled r for all studies was -0.57 (95% CI: -0.62, -0.52), indicating notable heterogeneity (Pcorrelation between the ADC and cellularity for brain tumors. There was no notable evidence of publication bias. There is a strong negative correlation between the ADC and tumor cellularity in patients, particularly in the brain. However, larger, prospective studies are warranted to validate these findings in other cancer types.

  19. A discrete model to study reaction-diffusion-mechanics systems.

    Science.gov (United States)

    Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V

    2011-01-01

    This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

  20. A discrete model to study reaction-diffusion-mechanics systems.

    Directory of Open Access Journals (Sweden)

    Louis D Weise

    Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

  1. Attractor of reaction-diffusion equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    José Valero

    2001-04-01

    Full Text Available In this paper we prove first some abstract theorems on existence of global attractors for differential inclusions generated by w-dissipative operators. Then these results are applied to reaction-diffusion equations in which the Babach space Lp is used as phase space. Finally, new results concerning the fractal dimension of the global attractor in the space L2 are obtained.

  2. Laser Spot Detection Based on Reaction Diffusion

    OpenAIRE

    Alejandro Vázquez-Otero; Danila Khikhlukha; J. M. Solano-Altamirano; Raquel Dormido; Natividad Duro

    2016-01-01

    Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presente...

  3. Mix and Inject: Reaction Initiation by Diffusion for Time-Resolved Macromolecular Crystallography

    Directory of Open Access Journals (Sweden)

    Marius Schmidt

    2013-01-01

    Full Text Available Time-resolved macromolecular crystallography unifies structure determination with chemical kinetics, since the structures of transient states and chemical and kinetic mechanisms can be determined simultaneously from the same data. To start a reaction in an enzyme, typically, an initially inactive substrate present in the crystal is activated. This has particular disadvantages that are circumvented when active substrate is directly provided by diffusion. However, then it is prohibitive to use macroscopic crystals because diffusion times become too long. With small micro- and nanocrystals diffusion times are adequately short for most enzymes and the reaction can be swiftly initiated. We demonstrate here that a time-resolved crystallographic experiment becomes feasible by mixing substrate with enzyme nanocrystals which are subsequently injected into the X-ray beam of a pulsed X-ray source.

  4. Signatures of a quantum diffusion limited hydrogen atom tunneling reaction.

    Science.gov (United States)

    Balabanoff, Morgan E; Ruzi, Mahmut; Anderson, David T

    2017-12-20

    We are studying the details of hydrogen atom (H atom) quantum diffusion in highly enriched parahydrogen (pH 2 ) quantum solids doped with chemical species in an effort to better understand H atom transport and reactivity under these conditions. In this work we present kinetic studies of the 193 nm photo-induced chemistry of methanol (CH 3 OH) isolated in solid pH 2 . Short-term irradiation of CH 3 OH at 1.8 K readily produces CH 2 O and CO which we detect using FTIR spectroscopy. The in situ photochemistry also produces CH 3 O and H atoms which we can infer from the post-photolysis reaction kinetics that display significant CH 2 OH growth. The CH 2 OH growth kinetics indicate at least three separate tunneling reactions contribute; (i) reactions of photoproduced CH 3 O with the pH 2 host, (ii) H atom reactions with the CH 2 O photofragment, and (iii) long-range migration of H atoms and reaction with CH 3 OH. We assign the rapid CH 2 OH growth to the following CH 3 O + H 2 → CH 3 OH + H → CH 2 OH + H 2 two-step sequential tunneling mechanism by conducting analogous kinetic measurements using deuterated methanol (CD 3 OD). By performing photolysis experiments at 1.8 and 4.3 K, we show the post-photolysis reaction kinetics change qualitatively over this small temperature range. We use this qualitative change in the reaction kinetics with temperature to identify reactions that are quantum diffusion limited. While these results are specific to the conditions that exist in pH 2 quantum solids, they have direct implications on the analogous low temperature H atom tunneling reactions that occur on metal surfaces and on interstellar grains.

  5. Multiscale simulations of anisotropic particles combining molecular dynamics and Green's function reaction dynamics

    NARCIS (Netherlands)

    Vijaykumar, A.; Ouldridge, T.E.; ten Wolde, P.R.; Bolhuis, P.G.

    2017-01-01

    The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic

  6. Molecules in motion: influences of diffusion on metabolic structure and function in skeletal muscle.

    Science.gov (United States)

    Kinsey, Stephen T; Locke, Bruce R; Dillaman, Richard M

    2011-01-15

    Metabolic processes are often represented as a group of metabolites that interact through enzymatic reactions, thus forming a network of linked biochemical pathways. Implicit in this view is that diffusion of metabolites to and from enzymes is very fast compared with reaction rates, and metabolic fluxes are therefore almost exclusively dictated by catalytic properties. However, diffusion may exert greater control over the rates of reactions through: (1) an increase in reaction rates; (2) an increase in diffusion distances; or (3) a decrease in the relevant diffusion coefficients. It is therefore not surprising that skeletal muscle fibers have long been the focus of reaction-diffusion analyses because they have high and variable rates of ATP turnover, long diffusion distances, and hindered metabolite diffusion due to an abundance of intracellular barriers. Examination of the diversity of skeletal muscle fiber designs found in animals provides insights into the role that diffusion plays in governing both rates of metabolic fluxes and cellular organization. Experimental measurements of metabolic fluxes, diffusion distances and diffusion coefficients, coupled with reaction-diffusion mathematical models in a range of muscle types has started to reveal some general principles guiding muscle structure and metabolic function. Foremost among these is that metabolic processes in muscles do, in fact, appear to be largely reaction controlled and are not greatly limited by diffusion. However, the influence of diffusion is apparent in patterns of fiber growth and metabolic organization that appear to result from selective pressure to maintain reaction control of metabolism in muscle.

  7. Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds

    KAUST Repository

    Desvillettes, Laurent; Fellner, Klemens

    2008-01-01

    In the continuation of [Desvillettes, L., Fellner, K.: Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations. J. Math. Anal. Appl. 319 (2006), no. 1, 157-176], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in L1 to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global L∞ bound via interpolation of a polynomially growing H1 bound with the almost exponential L1 convergence, and 3), finally, explicit exponential convergence to the steady state in all Sobolev norms.

  8. Numerical Analysis of Characteristics of Cellular Counterflow Diffusion Flames near Radiative Extinction Limit

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Su Ryong [Seoul National University of Technology, Seoul (Korea, Republic of)

    2014-06-15

    Nonlinear characteristics of cellular counterflow diffusion flame near the radiative extinction limit at large Damköhler number are numerically investigated. Lewis number is assumed to be 0.5 and flame evolution is calculated by imposing an infinitesimal disturbance to a one-dimensional(1-D) steady state flame. The early stage of nonlinear development is very similar to that predicted in a linear stability analysis. The disturbance with the wavenumber of the fastest growing mode emerges and grows gradually. Eventual, an alternating pattern of reacting and quenching stripes is developed. The cellular flame temperature is higher than that of 1-D flame because of the gain of the total enthalpy. As the Damköhler number is further increased, the shape of the cell becomes circular to increase the surface area per unit reacting volume. The cellular flames do not extinguish but survive even above the 1-D steady state extinction condition.

  9. Reaction and diffusion in turbulent combustion

    Energy Technology Data Exchange (ETDEWEB)

    Pope, S.B. [Mechanical and Aerospace Engineering, Ithaca, NY (United States)

    1993-12-01

    The motivation for this project is the need to obtain a better quantitative understanding of the technologically-important phenomenon of turbulent combustion. In nearly all applications in which fuel is burned-for example, fossil-fuel power plants, furnaces, gas-turbines and internal-combustion engines-the combustion takes place in a turbulent flow. Designers continually demand more quantitative information about this phenomenon-in the form of turbulent combustion models-so that they can design equipment with increased efficiency and decreased environmental impact. For some time the PI has been developing a class of turbulent combustion models known as PDF methods. These methods have the important virtue that both convection and reaction can be treated without turbulence-modelling assumptions. However, a mixing model is required to account for the effects of molecular diffusion. Currently, the available mixing models are known to have some significant defects. The major motivation of the project is to seek a better understanding of molecular diffusion in turbulent reactive flows, and hence to develop a better mixing model.

  10. Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case

    NARCIS (Netherlands)

    Bedeaux, D.; Ortiz de Zárate, J.M.; Pagonabarraga, I.; Sengers, J.V.; Kjelstrup, S.

    2011-01-01

    In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature

  11. Unified path integral approach to theories of diffusion-influenced reactions

    Science.gov (United States)

    Prüstel, Thorsten; Meier-Schellersheim, Martin

    2017-08-01

    Building on mathematical similarities between quantum mechanics and theories of diffusion-influenced reactions, we develop a general approach for computational modeling of diffusion-influenced reactions that is capable of capturing not only the classical Smoluchowski picture but also alternative theories, as is here exemplified by a volume reactivity model. In particular, we prove the path decomposition expansion of various Green's functions describing the irreversible and reversible reaction of an isolated pair of molecules. To this end, we exploit a connection between boundary value and interaction potential problems with δ - and δ'-function perturbation. We employ a known path-integral-based summation of a perturbation series to derive a number of exact identities relating propagators and survival probabilities satisfying different boundary conditions in a unified and systematic manner. Furthermore, we show how the path decomposition expansion represents the propagator as a product of three factors in the Laplace domain that correspond to quantities figuring prominently in stochastic spatially resolved simulation algorithms. This analysis will thus be useful for the interpretation of current and the design of future algorithms. Finally, we discuss the relation between the general approach and the theory of Brownian functionals and calculate the mean residence time for the case of irreversible and reversible reactions.

  12. Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients

    Directory of Open Access Journals (Sweden)

    Nauman Raza

    2013-01-01

    Full Text Available Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.

  13. WNT and DKK Determine Hair Follicle Spacing Through a Reaction-Diffusion Mechanism

    Science.gov (United States)

    Sick, Stefanie; Reinker, Stefan; Timmer, Jens; Schlake, Thomas

    2006-12-01

    Mathematical reaction-diffusion models have been suggested to describe formation of animal pigmentation patterns and distribution of epidermal appendages. However, the crucial signals and in vivo mechanisms are still elusive. Here we identify WNT and its inhibitor DKK as primary determinants of murine hair follicle spacing, using a combined experimental and computational modeling approach. Transgenic DKK overexpression reduces overall appendage density. Moderate suppression of endogenous WNT signaling forces follicles to form clusters during an otherwise normal morphogenetic program. These results confirm predictions of a WNT/DKK-specific mathematical model and provide in vivo corroboration of the reaction-diffusion mechanism for epidermal appendage formation.

  14. Graph Cellular Automata with Relation-Based Neighbourhoods of Cells for Complex Systems Modelling: A Case of Traffic Simulation

    Directory of Open Access Journals (Sweden)

    Krzysztof Małecki

    2017-12-01

    Full Text Available A complex system is a set of mutually interacting elements for which it is possible to construct a mathematical model. This article focuses on the cellular automata theory and the graph theory in order to compare various types of cellular automata and to analyse applications of graph structures together with cellular automata. It proposes a graph cellular automaton with a variable configuration of cells and relation-based neighbourhoods (r–GCA. The developed mechanism enables modelling of phenomena found in complex systems (e.g., transport networks, urban logistics, social networks taking into account the interaction between the existing objects. As an implementation example, modelling of moving vehicles has been made and r–GCA was compared to the other cellular automata models simulating the road traffic and used in the computer simulation process.

  15. Emergent structures in reaction-advection-diffusion systems on a sphere

    Science.gov (United States)

    Krause, Andrew L.; Burton, Abigail M.; Fadai, Nabil T.; Van Gorder, Robert A.

    2018-04-01

    We demonstrate unusual effects due to the addition of advection into a two-species reaction-diffusion system on the sphere. We find that advection introduces emergent behavior due to an interplay of the traditional Turing patterning mechanisms with the compact geometry of the sphere. Unidirectional advection within the Turing space of the reaction-diffusion system causes patterns to be generated at one point of the sphere, and transported to the antipodal point where they are destroyed. We illustrate these effects numerically and deduce conditions for Turing instabilities on local projections to understand the mechanisms behind these behaviors. We compare this behavior to planar advection which is shown to only transport patterns across the domain. Analogous transport results seem to hold for the sphere under azimuthal transport or away from the antipodal points in unidirectional flow regimes.

  16. Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

    Science.gov (United States)

    Simpson, Matthew J

    2015-01-01

    Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

  17. An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations

    KAUST Repository

    Burrage, Kevin

    2012-01-01

    Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids via robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed of the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator. © 2012 Society for Industrial and Applied Mathematics.

  18. Pattern dynamics of the reaction-diffusion immune system.

    Science.gov (United States)

    Zheng, Qianqian; Shen, Jianwei; Wang, Zhijie

    2018-01-01

    In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system.

  19. An improved cellular automata model for train operation simulation with dynamic acceleration

    Science.gov (United States)

    Li, Wen-Jun; Nie, Lei

    2018-03-01

    Urban rail transit plays an important role in the urban public traffic because of its advantages of fast speed, large transport capacity, high safety, reliability and low pollution. This study proposes an improved cellular automaton (CA) model by considering the dynamic characteristic of the train acceleration to analyze the energy consumption and train running time. Constructing an effective model for calculating energy consumption to aid train operation improvement is the basis for studying and analyzing energy-saving measures for urban rail transit system operation.

  20. Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations

    Science.gov (United States)

    Zhang, Linghai

    2017-10-01

    The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 traveling wave front as well as the existence and instability of a standing pulse solution if 0 traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.

  1. A reaction-diffusion model of CO2 influx into an oocyte

    Science.gov (United States)

    Somersalo, Erkki; Occhipinti, Rossana; Boron, Walter F.; Calvetti, Daniela

    2012-01-01

    We have developed and implemented a novel mathematical model for simulating transients in surface pH (pHS) and intracellular pH (pHi) caused by the influx of carbon dioxide (CO2) into a Xenopus oocyte. These transients are important tools for studying gas channels. We assume that the oocyte is a sphere surrounded by a thin layer of unstirred fluid, the extracellular unconvected fluid (EUF), which is in turn surrounded by the well-stirred bulk extracellular fluid (BECF) that represents an infinite reservoir for all solutes. Here, we assume that the oocyte plasma membrane is permeable only to CO2. In both the EUF and intracellular space, solute concentrations can change because of diffusion and reactions. The reactions are the slow equilibration of the CO2 hydration-dehydration reactions and competing equilibria among carbonic acid (H2CO3)/bicarbonate ( HCO3-) and a multitude of non-CO2/HCO3- buffers. Mathematically, the model is described by a coupled system of reaction-diffusion equations that—assuming spherical radial symmetry—we solved using the method of lines with appropriate stiff solvers. In agreement with experimental data (Musa-Aziz et al, PNAS 2009, 106:5406–5411), the model predicts that exposing the cell to extracellular 1.5% CO2/10 mM HCO3- (pH 7.50) causes pHi to fall and pHS to rise rapidly to a peak and then decay. Moreover, the model provides insights into the competition between diffusion and reaction processes when we change the width of the EUF, membrane permeability to CO2, native extra-and intracellular carbonic anhydrase-like activities, the non-CO2/HCO3- (intrinsic) intracellular buffering power, or mobility of intrinsic intracellular buffers. PMID:22728674

  2. On the effect of memory in a quantum prisoner's dilemma cellular automaton

    Science.gov (United States)

    Alonso-Sanz, Ramón; Revuelta, Fabio

    2018-03-01

    The disrupting effect of quantum memory on the dynamics of a spatial quantum formulation of the iterated prisoner's dilemma game with variable entangling is studied. The game is played within a cellular automata framework, i.e., with local and synchronous interactions. The main findings of this work refer to the shrinking effect of memory on the disruption induced by noise.

  3. A fractional reaction-diffusion description of supply and demand

    Science.gov (United States)

    Benzaquen, Michael; Bouchaud, Jean-Philippe

    2018-02-01

    We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the "square-root impact law"), as in the normal diffusion limit. However, the impact kernel decays as t-β with β = 1/2 in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent β takes any value in [0, 1/2], and can be tuned to match the empirical value β ≈ 1/4. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

  4. Dynamic Simulation of 1D Cellular Automata in the Active aTAM.

    Science.gov (United States)

    Jonoska, Nataša; Karpenko, Daria; Seki, Shinnosuke

    2015-07-01

    The Active aTAM is a tile based model for self-assembly where tiles are able to transfer signals and change identities according to the signals received. We extend Active aTAM to include deactivation signals and thereby allow detachment of tiles. We show that the model allows a dynamic simulation of cellular automata with assemblies that do not record the entire computational history but only the current updates of the states, and thus provide a way for (a) algorithmic dynamical structural changes in the assembly and (b) reusable space in self-assembly. The simulation is such that at a given location the sequence of tiles that attach and detach corresponds precisely to the sequence of states the synchronous cellular automaton generates at that location.

  5. Diffusion-weighted imaging for the cellularity assessment and matrix characterization of soft tissue tumour.

    Science.gov (United States)

    Robba, Tiziana; Chianca, Vito; Albano, Domenico; Clementi, Valeria; Piana, Raimondo; Linari, Alessandra; Comandone, Alessandro; Regis, Guido; Stratta, Maurizio; Faletti, Carlo; Borrè, Alda

    2017-11-01

    To evaluate whether apparent diffusion coefficient (ADC) of diffusion-weighted imaging (DWI) is able to investigate the histological features of soft tissue tumours. We reviewed MRIs of soft tissue tumours performed from 2012 to 2015 to calculate the average ADCs. We included 46 patients (27 male; mean age: 57 years, range 12-85 years) with histologically proven soft tissue tumours (10 benign, 2 intermediate 34 malignant) grouped into eight tumour type classes. An experienced pathologist assigned a semi-quantitative cellularity score (very high, high, medium and low) and tumour grading. The t test, ANOVA and linear regression were used to correlate ADC with clinicopathological data. Approximate receiver operating characteristic curves were created to predict possible uses of ADC to differentiate benign from malignant tumours. There was a significant difference (p < 0.01) in ADCs between these three groups excluding myxoid sarcomas. A significant difference was also evident between the tumour type classes (p < 0.001), grade II and III myxoid lesions (p < 0.05), tumour grading classes (p < 0.001) and cellularity scores classes (p < 0.001), with the lowest ADCs in the very high cellularity. While the linear regression analysis showed a significant relationship between ADC and tumour cellularity (r = 0.590, p ≤ 0.05) and grading (r = 0.437, p ≤ 0.05), no significant relationship was found with age, gender, tumour size and histological subtype. An optimal cut-off ADC value of 1.45 × 10 -3 mm 2 /s with 76.8% accuracy was found to differentiate benign from malignant tumours. DWI may offer adjunctive information about soft tissue tumours, but its clinical role is still to be defined.

  6. Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs

    Directory of Open Access Journals (Sweden)

    Bernard Girau

    2009-01-01

    and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.

  7. Car Deceleration Considering Its Own Velocity in Cellular Automata Model

    International Nuclear Information System (INIS)

    Li Keping

    2006-01-01

    In this paper, we propose a new cellular automaton model, which is based on NaSch traffic model. In our method, when a car has a larger velocity, if the gap between the car and its leading car is not enough large, it will decrease. The aim is that the following car has a buffer space to decrease its velocity at the next time, and then avoid to decelerate too high. The simulation results show that using our model, the car deceleration is realistic, and is closer to the field measure than that of NaSch model.

  8. Phase transitions enable computational universality in neuristor-based cellular automata

    International Nuclear Information System (INIS)

    Pickett, Matthew D; Stanley Williams, R

    2013-01-01

    We recently demonstrated that Mott memristors, two-terminal devices that exhibit threshold switching via an insulator to conductor phase transition, can serve as the active components necessary to build a neuristor, a biomimetic threshold spiking device. Here we extend those results to demonstrate, in simulation, neuristor-based circuits capable of performing general Boolean logic operations. We additionally show that these components can be used to construct a one-dimensional cellular automaton, rule 137, previously proven to be universal. This proof-of-principle shows that localized phase transitions can perform spiking computation, which is of particular interest for neuromorphic hardware. (paper)

  9. A fully coupled diffusion-reaction scheme for moisture sorption-desorption in an anhydride-cured epoxy resin

    KAUST Repository

    El Yagoubi, Jalal; Lubineau, Gilles; Roger, Frederic; Verdu, Jacques

    2012-01-01

    Thermoset materials frequently display non-classical moisture sorption behaviors. In this paper, we investigated this issue from an experimental point of view as well as in terms of modeling the water transport. We used the gravimetric technique to monitor water uptake by epoxy samples, with several thicknesses exposed to different levels of humidity during absorption and desorption tests. Our results revealed that the polymer displays a two-stage behavior with a residual amount of water that is desorbed progressively. We proposed a phenomenological reaction-diffusion scheme to describe this behavior. The model describes water transport as a competition between diffusion and the reaction, during which the local diffusivity and solubility depend on the local advancement of the reaction. We then implemented our model using COMSOL Multiphysics and identified it using a MATLAB-COMSOL optimization tool and the experimental data. We discussed the relation between the hydrophilicity of the product of the reaction and the diffusion behavior. We examined the reaction-induced modification of the water concentration field. It is worth noting that part of the phenomenology can be explained by the presence of hydrolyzable groups. © 2012 Elsevier Ltd. All rights reserved.

  10. Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

    Directory of Open Access Journals (Sweden)

    Matthew J Simpson

    Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0diffusivity associated with the spreading density profile, (iii the reaction rate, and (iv the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t.

  11. A fully coupled diffusion-reaction scheme for moisture sorption-desorption in an anhydride-cured epoxy resin

    KAUST Repository

    El Yagoubi, Jalal

    2012-11-01

    Thermoset materials frequently display non-classical moisture sorption behaviors. In this paper, we investigated this issue from an experimental point of view as well as in terms of modeling the water transport. We used the gravimetric technique to monitor water uptake by epoxy samples, with several thicknesses exposed to different levels of humidity during absorption and desorption tests. Our results revealed that the polymer displays a two-stage behavior with a residual amount of water that is desorbed progressively. We proposed a phenomenological reaction-diffusion scheme to describe this behavior. The model describes water transport as a competition between diffusion and the reaction, during which the local diffusivity and solubility depend on the local advancement of the reaction. We then implemented our model using COMSOL Multiphysics and identified it using a MATLAB-COMSOL optimization tool and the experimental data. We discussed the relation between the hydrophilicity of the product of the reaction and the diffusion behavior. We examined the reaction-induced modification of the water concentration field. It is worth noting that part of the phenomenology can be explained by the presence of hydrolyzable groups. © 2012 Elsevier Ltd. All rights reserved.

  12. The cellular environment in computer simulations of radiation-induced damage to DNA

    International Nuclear Information System (INIS)

    Moiseenko, V.V.; Waker, A.J.; Prestwich, W.V.

    1998-01-01

    Radiation-induced DNA single- and double-strand breaks were modeled for 660 keV photon radiation and scavenger capacity mimicking the cellular environment. Atomistic representation of DNA in B form with a first hydration shell was utilized to model direct and indirect damage. Monte Carlo generated electron tracks were used to model energy deposition in matter and to derive initial spatial distributions of species which appear in the medium following radiolysis. Diffusion of species was followed with time, and their reactions with DNA and each other were modeled in an encounter-controlled manner. Three methods to account for hydroxyl radical diffusion in a cellular environment were tested: assumed exponential survival, time-limited modeling and modeling of reactions between hydroxyl radicals and scavengers in an encounter-controlled manner. Although the method based on modeling scavenging in an encounter-controlled manner is more precise, it requires substantially more computer resources than either the exponential or time-limiting method. Scavenger concentrations of 0.5 and 0.15 M were considered using exponential and encounter-controlled methods with reaction rate set at 3 x 10 9 dm 3 mol -1 s -1 . Diffusion length and strand break yields, predicted by these two methods for the same scavenger molarity, were different by 20%-30%. The method based on limiting time of chemistry follow-up to 10 -9 s leads to DNA damage and radical diffusion estimates similar to 0.5 M scavenger concentration in the other two methods. The difference observed in predictions made by the methods considered could be tolerated in computer simulations of DNA damage. (orig.)

  13. The cellular environment in computer simulations of radiation-induced damage to DNA

    International Nuclear Information System (INIS)

    Moiseenko, V.V.; Hamm, R.N.; Waker, A.J.; Prestwich, W.V.

    1988-01-01

    Radiation-induced DNA single- and double-strand breaks were modeled for 660 keV photon radiation and scavenger capacity mimicking the cellular environment. Atomistic representation of DNA in B form with a first hydration shell was utilized to model direct and indirect damage. Monte Carlo generated electron tracks were used to model energy deposition in matter and to derive initial spatial distributions of species which appear in the medium following radiolysis. Diffusion of species was followed with time, and their reactions with DNA and each other were modeled in an encounter-controlled manner. Three methods to account for hydroxyl radical diffusion in cellular environment were tested: assumed exponential survival, time-limited modeling and modeling of reactions between hydroxyl radicals and scavengers in an encounter-controlled manner. Although the method based on modeling scavenging in an encounter-controlled manner is more precise, it requires substantially more computer resources than either the exponential or time-limiting method. Scavenger concentrations of 0.5 and 0.15 M were considered using exponential and encounter-controlled methods with reaction rate set at 3x10 9 dm 3 mol -1 s-1. Diffusion length and strand break yields, predicted by these two methods for the same scavenger molarity, were different by 20%-30%. The method based on limiting time of chemistry follow-up to 10 -9 s leads to DNA damage and radical diffusion estimates similar to 0.5 M scavenger concentration in the other two methods. The difference observed in predictions made by the methods considered could be tolerated in computer simulations of DNA damage. (author)

  14. Global dynamics of a reaction-diffusion system

    Directory of Open Access Journals (Sweden)

    Yuncheng You

    2011-02-01

    Full Text Available In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown.

  15. A Universal Semi-totalistic Cellular Automaton on Kite and Dart Penrose Tilings

    Directory of Open Access Journals (Sweden)

    Katsunobu Imai

    2012-08-01

    Full Text Available In this paper we investigate certain properties of semi-totalistic cellular automata (CA on the well known quasi-periodic kite and dart two dimensional tiling of the plane presented by Roger Penrose. We show that, despite the irregularity of the underlying grid, it is possible to devise a semi-totalistic CA capable of simulating any boolean circuit on this aperiodic tiling.

  16. Diffuse Urticarial Reaction Associated with Titanium Dioxide Following Laser Tattoo Removal Treatments.

    Science.gov (United States)

    Willardson, Hal Bret; Kobayashi, Todd T; Arnold, Jason G; Hivnor, Chad M; Bowen, Casey D

    2017-03-01

    Local and generalized allergic reactions following laser tattoo removal have been documented, but are rare. To our knowledge, this is the fourth documented case of widespread urticarial eruptions following laser tattoo removal treatment. Unlike previously documented cases, this patient's reaction was found to be associated with titanium dioxide within the tattoo and her symptoms were recalcitrant to medical therapy. A 46-year-old female experienced diffuse urticarial plaques, erythema, and pruritis following multiple laser tattoo removal treatments with an Nd:YAG laser. The systemic allergic reaction was recalcitrant to increasing doses of antihistamines and corticosteroids. The tattoo was finally surgically excised. The excised tissue was analyzed by scanning electron microscopy and energy-dispersive X-ray analysis and contained high levels of titanium dioxide. Two weeks following the excision, and without the use of medical therapy, the patient had complete resolution of her generalized urticaria. Ours is the first documented case of a diffuse urticarial reaction following laser tattoo removal treatments that shows a strong association to titanium dioxide within the tattoo pigment. Herein, we describe a novel surgical approach to treat recalcitrant generalized allergic reaction to tattoo pigment.

  17. Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

    KAUST Repository

    Woolley, Thomas E.; Baker, Ruth E.; Gaffney, Eamonn A.; Maini, Philip K.; Seirin-Lee, Sungrim

    2012-01-01

    Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.

  18. Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

    KAUST Repository

    Woolley, Thomas E.

    2012-05-22

    Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.

  19. Simulation of reaction diffusion processes over biologically relevant size and time scales using multi-GPU workstations.

    Science.gov (United States)

    Hallock, Michael J; Stone, John E; Roberts, Elijah; Fry, Corey; Luthey-Schulten, Zaida

    2014-05-01

    Simulation of in vivo cellular processes with the reaction-diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel e ciency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli . Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems.

  20. The effect of cellular aging on the dynamics of spiral waves

    International Nuclear Information System (INIS)

    Deng Min-Yi; Chen Xi-Qiong; Tang Guo-Ning

    2014-01-01

    Cellular aging can result in deterioration of electrical coupling, the extension of the action potential duration, and lower excitability of the cell. Those factors are introduced into the Greenberg—Hastings cellular automaton model and the effects of the cellular aging on the dynamics of spiral waves are studied. The numerical results show that a 50% reduction of the coupling strength of aging cells has a little influence on spiral waves. If the coupling strength of aging cells equals zero, the ability for the medium to maintain spiral waves will be reduced by approximately 50% when the aging cell ratio increases from 0 to 0.5, where the reduction of cell excitability plays a major role in inducing disappearance of spiral waves. When the relevant parameters are properly chosen, the cellular aging can lead to the meandering of spiral waves, the emergence of the binary spiral waves, and even the disappearance of spiral waves via the stopping rotation or shrinkage of wave. Physical mechanisms of the above phenomena are analyzed briefly. (general)

  1. Dynamic phase transition in diffusion-limited reactions

    International Nuclear Information System (INIS)

    Tauber, U.C.

    2002-01-01

    Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means of the renormalization group. The resulting universality classes for single-species systems are reviewed here. Generically, the critical exponents are those of directed percolation (Reggeon field theory), with critical dimension d c = 4. Yet local particle number parity conservation in even-offspring branching and annihilating random walks implies an inactive phase (emerging below d c = 4/3) that is characterized by the power laws of the pair annihilation reaction, and leads to different critical exponents at the transition. For local processes without memory, the pair contact process with diffusion represents the only other non-trivial universality class. The consistent treatment of restricted site occupations and quenched random reaction rates are important open issues (Author)

  2. Study of Drying Shrinkage Cracking by Lattice Gas Automaton and Environmental Scanning Electron Microscope

    NARCIS (Netherlands)

    Van Mier, J.G.M.; Jankovic, D.

    2005-01-01

    Numerical modeling of moisture flow, drying shrinkage and crack phenomena in cement microstructure, by coupling a Lattice Gas Automaton and a Lattice Fracture Model, highlighted the importance of a shrinkage coefficient (?sh) as the most significant parameter for achieving realistic numerical

  3. Efficient kinetic Monte Carlo method for reaction-diffusion problems with spatially varying annihilation rates

    Science.gov (United States)

    Schwarz, Karsten; Rieger, Heiko

    2013-03-01

    We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.

  4. Cellular automaton model for hydrogen transport dynamics through metallic surface

    International Nuclear Information System (INIS)

    Shimura, K.; Yamaguchi, K.; Terai, T.; Yamawaki, M.

    2002-01-01

    Hydrogen re-emission and re-combination at the surface of first wall materials are a crucial issue for the understanding of the fuel recycling and for the tritium inventory in plasma facing materials. It is know to be difficult to model the transient behaviour of those processes due to their complex time-transient nature. However, cellular automata (CA) are powerful tools to model such complex systems because of their nature of discreteness in both dependent and independent variables. Then the system can be represented by the fully local interactions between cells. For that reason, complex physical and chemical systems can be described by fairly simple manner. In this study, the kinetics of desorption of adsorbed hydrogen from an ideal metallic surface is modelled in CA. Thermal desorption is simulated with this model and the comparison with the theory of rate processes is performed to identify the validity of this model. The overall results show that this model is reasonable to express the desorption kinetics

  5. Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.

    Science.gov (United States)

    Wang, Kaier; Steyn-Ross, Moira L; Steyn-Ross, D Alistair; Wilson, Marcus T; Sleigh, Jamie W; Shiraishi, Yoichi

    2014-04-11

    Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming

  6. Reaction diffusion voronoi diagrams: from sensors data to computing

    Czech Academy of Sciences Publication Activity Database

    Vázquez-Otero, Alejandro (ed.); Faigl, J.; Dormido, R.; Duro, N.

    2015-01-01

    Roč. 15, č. 6 (2015), s. 12736-12764 ISSN 1424-8220 R&D Projects: GA MŠk ED1.1.00/02.0061 Grant - others:ELI Beamlines(XE) CZ.1.05/1.1.00/02.0061 Institutional support: RVO:68378271 Keywords : reaction diffusion * FitzHugh–Nagumo * path planning * navigation * exploration Subject RIV: BD - Theory of Information Impact factor: 2.033, year: 2015

  7. Evolution of Cellular Automata toward a LIFE-Like Rule Guided by 1/ƒ Noise

    Science.gov (United States)

    Ninagawa, Shigeru

    There is evidence in favor of a relationship between the presence of 1/ƒ noise and computational universality in cellular automata. To confirm the relationship, we search for two-dimensional cellular automata with a 1/ƒ power spectrum by means of genetic algorithms. The power spectrum is calculated from the evolution of the state of the cell, starting from a random initial configuration. The fitness is estimated by the power spectrum with consideration of the spectral similarity to the 1/ƒ spectrum. The result shows that the rule with the highest fitness over the most runs exhibits a 1/ƒ type spectrum and its transition function and behavior are quite similar to those of the Game of Life, which is known to be a computationally universal cellular automaton. These results support the relationship between the presence of 1/ƒ noise and computational universality.

  8. Evolution of density profiles for reaction-diffusion processes

    International Nuclear Information System (INIS)

    Ondarza-Rovira, R.

    1990-01-01

    The purpose of this work is to study the reaction diffusion equations for the concentration of one species in one spatial dimension. Nonlinear diffusion equations paly an important role in several fields: Physics, Kinetic Chemistry, Poblational Biology, Neurophysics, etc. The study of the behavior of solutions, with nonlinear diffusion coefficient, and monomial creation and annihilation terms, is considered. It is found, that when the exponent of the annihilation term is smaller than the one of the creation term, unstable equilibrium solutions may exist, for which solutions above it explode in finite time, but solutions below it decay exponentially. By means of the reduction to quadratures technique, it is found that is possible to obtain travelling wave solution in those cases when the annihilation term is greater than the creation term. This method of solution always permits to know the propagation velocity of the front, even if the concentration cannot be written in closed form. The portraits of the solutions in phase space show the existence of solutions which velocities may be smaller or greater than the ones found analytically. Linear and nonlinear diffusion equations, differ significantly in that the former are of change of solutions are considered. This is reminiscent of the fact that linear diffusion yields infinite propagation speed, even though the speed of the front is finite. When the strength of the annihilation term increases, as compared with that of the creation term, arbitrary initial conditions (studied numerically) relax to stable platforms that move indefinitly with constant speed. (Author)

  9. Externally controlled anisotropy in pattern-forming reaction-diffusion systems.

    Science.gov (United States)

    Escala, Dario M; Guiu-Souto, Jacobo; Muñuzuri, Alberto P

    2015-06-01

    The effect of centrifugal forces is analyzed in a pattern-forming reaction-diffusion system. Numerical simulations conducted on the appropriate extension of the Oregonator model for the Belousov-Zhabotinsky reaction show a great variety of dynamical behaviors in such a system. In general, the system exhibits an anisotropy that results in new types of patterns or in a global displacement of the previous one. We consider the effect of both constant and periodically modulated centrifugal forces on the different types of patterns that the system may exhibit. A detailed analysis of the patterns and behaviors observed for the different parameter values considered is presented here.

  10. Modeling of Reaction Processes Controlled by Diffusion

    International Nuclear Information System (INIS)

    Revelli, Jorge

    2003-01-01

    Stochastic modeling is quite powerful in science and technology.The technics derived from this process have been used with great success in laser theory, biological systems and chemical reactions.Besides, they provide a theoretical framework for the analysis of experimental results on the field of particle's diffusion in ordered and disordered materials.In this work we analyze transport processes in one-dimensional fluctuating media, which are media that change their state in time.This fact induces changes in the movements of the particles giving rise to different phenomena and dynamics that will be described and analyzed in this work.We present some random walk models to describe these fluctuating media.These models include state transitions governed by different dynamical processes.We also analyze the trapping problem in a lattice by means of a simple model which predicts a resonance-like phenomenon.Also we study effective diffusion processes over surfaces due to random walks in the bulk.We consider different boundary conditions and transitions movements.We derive expressions that describe diffusion behaviors constrained to bulk restrictions and the dynamic of the particles.Finally it is important to mention that the theoretical results obtained from the models proposed in this work are compared with Monte Carlo simulations.We find, in general, excellent agreements between the theory and the simulations

  11. Research of the method of pseudo-random number generation based on asynchronous cellular automata with several active cells

    Directory of Open Access Journals (Sweden)

    Bilan Stepan

    2017-01-01

    Full Text Available To date, there are many tasks that are aimed at studying the dynamic changes in physical processes. These tasks do not give advance known result. The solution of such problems is based on the construction of a dynamic model of the object. Successful structural and functional implementation of the object model can give a positive result in time. This approach uses the task of constructing artificial biological objects. To solve such problems, pseudo-random number generators are used, which also find wide application for information protection tasks. Such generators should have good statistical properties and give a long repetition period of the generated pseudo-random bit sequence. This work is aimed at improving these characteristics. The paper considers the method of forming pseudo-random sequences of numbers on the basis of aperiodic cellular automata with two active cells. A pseudo-random number generator is proposed that generates three bit sequences. The first two bit sequences are formed by the corresponding two active cells in the cellular automaton. The third bit sequence is the result of executing the XOR function over the bits of the first two sequences and it has better characteristics compared to them. The use of cellular automata with two active cells allowed to improve the statistical properties of the formed bit sequence, as well as its repetition period. This is proved by using graphical tests for generators built based on cellular automata using the neighborhoods of von Neumann and Moore. The tests showed high efficiency of the generator based on an asynchronous cellular automaton with the neighborhood of Moore. The proposed pseudo-random number generators have good statistical properties, which makes it possible to use them in information security systems, as well as for simulation tasks of various dynamic processes.

  12. Existence of global solutions to reaction-diffusion systems via a Lyapunov functional

    Directory of Open Access Journals (Sweden)

    Said Kouachi

    2001-10-01

    Full Text Available The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations which give $L^{p}$-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11].

  13. Mass transfer rate through liquid membranes: interfacial chemical reactions and diffusion as simultaneous permeability controlling factors

    International Nuclear Information System (INIS)

    Danesi, P.R.; Horwitz, E.P.; Vandegrift, G.F.; Chiarizia, R.

    1981-01-01

    Equations describing the permeability of a liquid membrane to metal cations have been derived taking into account aqueous diffusion, membrane diffusion, and interfacial chemical reactions as simultaneous permeability controlling factors. Diffusion and chemical reactions have been coupled by a simple model analogous to the one previously described by us to represent liquid-liquid extraction kinetics. The derived equations, which make use of experimentally determined interfacial reaction mechanisms, qualitatively fit unexplained literature data regarding Cu 2+ transfer through liquid membranes. Their use to predict and optimize membrane permeability in practical separation processes by setting the appropriate concentration of the membrane carrier [LIX 64 (General Mills), a commercial β-hydroxy-oxime] and the pH of the aqueous copper feed solution is briefly discussed. 4 figures

  14. From QCA (Quantum Cellular Automata) to Organocatalytic Reactions with Stabilized Carbenium Ions.

    Science.gov (United States)

    Gualandi, Andrea; Mengozzi, Luca; Manoni, Elisabetta; Giorgio Cozzi, Pier

    2016-06-01

    What do quantum cellular automata (QCA), "on water" reactions, and SN 1-type organocatalytic transformations have in common? The link between these distant arguments is the practical access to useful intermediates and key products through the use of stabilized carbenium ions. Over 10 years, starting with a carbenium ion bearing a ferrocenyl group, to the 1,3-benzodithiolylium carbenium ion, our group has exploited the use of these intermediates in useful and practical synthetic transformations. In particular, we have applied the use of carbenium ions to stereoselective organocatalytic alkylation reactions, showing a possible solution for the "holy grail of organocatalysis". Examples of the use of these quite stabilized intermediates are now also considered in organometallic chemistry. On the other hand, the stable carbenium ions are also applied to tailored molecules adapted to quantum cellular automata, a new possible paradigm for computation. Carbenium ions are not a problem, they can be a/the solution! © 2016 The Chemical Society of Japan & Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

  15. Continuous Dependence in Front Propagation for Convective Reaction-Diffusion Models with Aggregative Movements

    Directory of Open Access Journals (Sweden)

    Luisa Malaguti

    2011-01-01

    Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.

  16. Stochastic processes, multiscale modeling, and numerical methods for computational cellular biology

    CERN Document Server

    2017-01-01

    This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of s...

  17. On the solutions of fractional reaction-diffusion equations

    Directory of Open Access Journals (Sweden)

    Jagdev Singh

    2013-05-01

    Full Text Available In this paper, we obtain the solution of a fractional reaction-diffusion equation associated with the generalized Riemann-Liouville fractional derivative as the time derivative and Riesz-Feller fractional derivative as the space-derivative. The results are derived by the application of the Laplace and Fourier transforms in compact and elegant form in terms of Mittag-Leffler function and H-function. The results obtained here are of general nature and include the results investigated earlier by many authors.

  18. Exact substitute processes for diffusion-reaction systems with local complete exclusion rules

    International Nuclear Information System (INIS)

    Schulz, Michael; Reineker, Peter

    2005-01-01

    Lattice systems with one species diffusion-reaction processes under local complete exclusion rules are studied analytically starting from the usual master equations with discrete variables and their corresponding representation in a Fock space. On this basis, a formulation of the transition probability as a Grassmann path integral is derived in a straightforward manner. It will be demonstrated that this Grassmann path integral is equivalent to a set of Ito stochastic differential equations. Averages of arbitrary variables and correlation functions of the underlying diffusion-reaction system can be expressed as weighted averages over all solutions of the system of stochastic differential equations. Furthermore, these differential equations are equivalent to a Fokker-Planck equation describing the probability distribution of the actual Ito solutions. This probability distribution depends on continuous variables in contrast to the original master equation, and their stochastic dynamics may be interpreted as a substitute process which is completely equivalent to the original lattice dynamics. Especially, averages and correlation functions of the continuous variables are connected to the corresponding lattice quantities by simple relations. Although the substitute process for diffusion-reaction systems with exclusion rules has some similarities to the well-known substitute process for the same system without exclusion rules, there exists a set of remarkable differences. The given approach is not only valid for the discussed single-species processes. We give sufficient arguments to show that arbitrary combinations of unimolecular and bimolecular lattice reactions under complete local exclusions may be described in terms of our approach

  19. Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

    Science.gov (United States)

    Indekeu, Joseph O.; Smets, Ruben

    2017-08-01

    Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

  20. Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

    International Nuclear Information System (INIS)

    Indekeu, Joseph O; Smets, Ruben

    2017-01-01

    Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically. (paper)

  1. An analytic algorithm for the space-time fractional reaction-diffusion equation

    Directory of Open Access Journals (Sweden)

    M. G. Brikaa

    2015-11-01

    Full Text Available In this paper, we solve the space-time fractional reaction-diffusion equation by the fractional homotopy analysis method. Solutions of different examples of the reaction term will be computed and investigated. The approximation solutions of the studied models will be put in the form of convergent series to be easily computed and simulated. Comparison with the approximation solution of the classical case of the studied modeled with their approximation errors will also be studied.

  2. One-dimensional isothermal multicomponent diffusion-reaction model and its application to methanol synthesis over commercial Cu-based catalyst

    Directory of Open Access Journals (Sweden)

    Lei Kun

    2015-03-01

    Full Text Available The present work was a study on global reaction rate of methanol synthesis. We measured experimentally the global reaction rate in the internal recycle gradientless reactor over catalyst SC309. The diffusion-reaction model of methanol synthesis was suggested. For model we chose the hydrogenation of CO and CO2 as key reaction. CO and CO2 were key components in our model. The internal diffusion effectiveness factors of CO and CO2 in the catalyst were calculated by the numerical integration. A comparison with the experiment showed that all the absolute values of the relative error were less than 10%. The simulation results showed that decreasing reaction temperature and catalyst diameter were conducive to reduce the influence of the internal diffusion on the methanol synthesis.

  3. On some limitations of reaction-diffusion chemical computers in relation to Voronoi diagram and its inversion

    International Nuclear Information System (INIS)

    Adamatzky, Andrew; Lacy Costello, Benjamin de

    2003-01-01

    A reaction-diffusion chemical computer in this context is a planar uniform chemical reactor, where data and results of a computation are represented by concentration profiles of reactants and the computation itself is implemented via the spreading and interaction of diffusive and phase waves. This class of chemical computers are efficient at solving problems with a 'natural' parallelism where data sets are decomposable onto a large number of geographically neighboring domains which are then processed in parallel. Typical problems of this type include image processing, geometrical transformations and optimisation. When chemical based devices are used to solve such problems questions regarding their reproducible, efficiency and the accuracy of their computations arise. In addition to these questions what are the limitations of reaction-diffusion chemical processors--what type of problems cannot currently and are unlikely ever to be solved? To answer the questions we study how a Voronoi diagram is constructed and how it is inverted in a planar chemical processor. We demonstrate that a Voronoi diagram is computed only partially in the chemical processor. We also prove that given a specific Voronoi diagram it is impossible to reconstruct the planar set (from which diagram was computed) in the reaction-diffusion chemical processor. In the Letter we open the first ever line of enquiry into the computational inability of reaction-diffusion chemical computers

  4. Digitally programmable microfluidic automaton for multiscale combinatorial mixing and sample processing†

    Science.gov (United States)

    Jensen, Erik C.; Stockton, Amanda M.; Chiesl, Thomas N.; Kim, Jungkyu; Bera, Abhisek; Mathies, Richard A.

    2013-01-01

    A digitally programmable microfluidic Automaton consisting of a 2-dimensional array of pneumatically actuated microvalves is programmed to perform new multiscale mixing and sample processing operations. Large (µL-scale) volume processing operations are enabled by precise metering of multiple reagents within individual nL-scale valves followed by serial repetitive transfer to programmed locations in the array. A novel process exploiting new combining valve concepts is developed for continuous rapid and complete mixing of reagents in less than 800 ms. Mixing, transfer, storage, and rinsing operations are implemented combinatorially to achieve complex assay automation protocols. The practical utility of this technology is demonstrated by performing automated serial dilution for quantitative analysis as well as the first demonstration of on-chip fluorescent derivatization of biomarker targets (carboxylic acids) for microchip capillary electrophoresis on the Mars Organic Analyzer. A language is developed to describe how unit operations are combined to form a microfluidic program. Finally, this technology is used to develop a novel microfluidic 6-sample processor for combinatorial mixing of large sets (>26 unique combinations) of reagents. The digitally programmable microfluidic Automaton is a versatile programmable sample processor for a wide range of process volumes, for multiple samples, and for different types of analyses. PMID:23172232

  5. Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems

    International Nuclear Information System (INIS)

    Owolabi, Kolade M.

    2016-01-01

    The aim of this paper is to examine pattern formation in the sub— and super-diffusive scenarios and compare it with that of classical or standard diffusive processes in two-component fractional reaction-diffusion systems that modeled a predator-prey dynamics. The focus of the work concentrates on the use of two separate mathematical techniques, we formulate a Fourier spectral discretization method as an efficient alternative technique to solve fractional reaction-diffusion problems in higher-dimensional space, and later advance the resulting systems of ODEs in time with the adaptive exponential time-differencing solver. Obviously, the fractional Fourier approach is able to achieve spectral convergence up to machine precision regardless of the fractional order α, owing to the fact that our approach is able to give full diagonal representation of the fractional operator. The complexity of the dynamics in this system is theoretically discussed and graphically displayed with some examples and numerical simulations in one, two and three dimensions.

  6. The Induced Dimension Reduction method applied to convection-diffusion-reaction problems

    NARCIS (Netherlands)

    Astudillo, R.; Van Gijzen, M.B.

    2016-01-01

    Discretization of (linearized) convection-diffusion-reaction problems yields a large and sparse non symmetric linear system of equations, Ax = b. (1) In this work, we compare the computational behavior of the Induced Dimension Reduction method (IDR(s)) [10], with other short-recurrences Krylov

  7. Towards reaction-diffusion computing devices based on minority-carrier transport in semiconductors

    International Nuclear Information System (INIS)

    Asai, Tetsuya; Adamatzky, Andrew; Amemiya, Yoshihito

    2004-01-01

    Reaction-diffusion (RD) chemical systems are known to realize sensible computation when both data and results of the computation are encoded in concentration profiles of chemical species; the computation is implemented via spreading and interaction of either diffusive or phase waves. Thin-layer chemical systems are thought of therefore as massively-parallel locally-connected computing devices, where micro-volume of the medium is analogous to an elementary processor. Practical applications of the RD chemical systems are reduced however due to very low speed of traveling waves which makes real-time computation senseless. To overcome the speed-limitations while preserving unique features of RD computers we propose a semiconductor RD computing device where minority carriers diffuse as chemical species and reaction elements are represented by p-n-p-n diodes. We offer blue-prints of the RD semiconductor devices, and study in computer simulation propagation phenomena of the density wave of minority carriers. We then demonstrate what computational problems can be solved in RD semiconductor devices and evaluate space-time complexity of computation in the devices

  8. An Application of Equivalence Transformations to Reaction Diffusion Equations

    Directory of Open Access Journals (Sweden)

    Mariano Torrisi

    2015-10-01

    Full Text Available In this paper, we consider a quite general class of advection reaction diffusion systems. By using an equivalence generator, derived in a previous paper, the authors apply a projection theorem to determine some special forms of the constitutive functions that allow the extension by one of the two-dimensional principal Lie algebra. As an example, a special case is discussed at the end of the paper.

  9. Multiple Scale Reaction-Diffusion-Advection Problems with Moving Fronts

    Science.gov (United States)

    Nefedov, Nikolay

    2016-06-01

    In this work we discuss the further development of the general scheme of the asymptotic method of differential inequalities to investigate stability and motion of sharp internal layers (fronts) for nonlinear singularly perturbed parabolic equations, which are called in applications reaction-diffusion-advection equations. Our approach is illustrated for some new important cases of initial boundary value problems. We present results on stability and on the motion of the fronts.

  10. Effects of fexofenadine and hydroxyzine on brake reaction time during car-driving with cellular phone use.

    Science.gov (United States)

    Tashiro, Manabu; Horikawa, Etsuo; Mochizuki, Hideki; Sakurada, Yumiko; Kato, Motohisa; Inokuchi, Takatoshi; Ridout, Fran; Hindmarch, Ian; Yanai, Kazuhiko

    2005-10-01

    Antihistamines are a mainstay treatment for allergic rhinitis; however, many older agents cause adverse events, including sedation and central nervous system (CNS) impairment. Research has shown sedating effects of antihistamines on driving; currently, no known study has examined whether cellular phone usage while driving further compounds impairment in individuals administered antihistamines. The aim of this study was to examine this endpoint. In a randomized, double-blind, placebo-controlled, three-way crossover study, healthy volunteers received fexofenadine HCl 120 mg, hydroxyzine HCl 30 mg and placebo. Brake reaction time (BRT) was used to examine driving performance across four conditions: driving only; driving while completing simple calculations; complex calculations; and conversing on a cellular phone. Subjective sedation assessments were also conducted. Brake reaction time with and without cellular phone usage in fexofenadine-treated subjects did not differ significantly from placebo in any condition. In contrast, hydroxyzine-treated subjects were significantly more sedated and had slower BRTs, suggesting slower hazard recognition and brake application, compared with the fexofenadine and placebo groups in all conditions. Importantly, cellular phone operation was an additive factor, increasing BRTs in hydroxyzine-treated volunteers. Fexofenadine did not impair CNS function in subjects involved in a divided attention task of driving and cellular phone operation. Copyright (c) 2005 John Wiley & Sons, Ltd.

  11. Exponential growth for self-reproduction in a catalytic reaction network: relevance of a minority molecular species and crowdedness

    Science.gov (United States)

    Kamimura, Atsushi; Kaneko, Kunihiko

    2018-03-01

    Explanation of exponential growth in self-reproduction is an important step toward elucidation of the origins of life because optimization of the growth potential across rounds of selection is necessary for Darwinian evolution. To produce another copy with approximately the same composition, the exponential growth rates for all components have to be equal. How such balanced growth is achieved, however, is not a trivial question, because this kind of growth requires orchestrated replication of the components in stochastic and nonlinear catalytic reactions. By considering a mutually catalyzing reaction in two- and three-dimensional lattices, as represented by a cellular automaton model, we show that self-reproduction with exponential growth is possible only when the replication and degradation of one molecular species is much slower than those of the others, i.e., when there is a minority molecule. Here, the synergetic effect of molecular discreteness and crowding is necessary to produce the exponential growth. Otherwise, the growth curves show superexponential growth because of nonlinearity of the catalytic reactions or subexponential growth due to replication inhibition by overcrowding of molecules. Our study emphasizes that the minority molecular species in a catalytic reaction network is necessary for exponential growth at the primitive stage of life.

  12. Reaction layer in U-7WT%MO/Al diffusion couples

    International Nuclear Information System (INIS)

    Mirandou, M.I.; Balart, S.N.; Ortiz, M.; Granovsky, M.S.

    2003-01-01

    New results of the reaction layer characterization between γ (U-7wt%Mo) alloy and Al, in chemical diffusion couples, are presented. The analysis was performed using optical and scanning electron microscopy with EDAX and X-ray diffraction techniques. Besides the main components (U, Mo)Al 3 and (U, Mo)Al 4 , already reported, two ternary compounds of high Al content have been identified in the reaction layer when it grew in retained or decomposed γ (U, Mo) phase, respectively. The drastic consequence on the interdiffusion behavior due to the thermal instability of the retained γ (U, Mo) phase is discussed. (author)

  13. Cellular structure of lean hydrogen flames in microgravity

    Science.gov (United States)

    Patnaik, G.; Kailasanath, K.

    1990-01-01

    Detailed, time-dependent, two-dimensional numerical simulations of premixed laminar flames have been used to study the initiation and subsequent development of cellular structures in lean hydrogen-air flames. The model includes detailed hydrogen-oxygen combustion with 24 elementary reactions of eight reactive species and a nitrogen diluent, molecular diffusion of all species, thermal conduction, viscosity, and convection. This model has been used to study the nonlinear evolution of cellular flame structure and shows that cell splitting, as observed in experiments, can be predicted numerically for sufficiently reactive mixtures. The structures that evolved also resembled the cellular structures observed in experiments. The present study shows that the 'cell-split limit' postulated from experimental observations is an intrinsic property of the mixture and that external factors such as heat losses are not necessary to cause this limit.

  14. Competitive autocatalytic reactions in chaotic flows with diffusion: Prediction using finite-time Lyapunov exponents

    International Nuclear Information System (INIS)

    Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.

    2014-01-01

    We investigate chaotic advection and diffusion in autocatalytic reactions for time-periodic sine flow computationally using a mapping method with operator splitting. We specifically consider three different autocatalytic reaction schemes: a single autocatalytic reaction, competitive autocatalytic reactions, which can provide insight into problems of chiral symmetry breaking and homochirality, and competitive autocatalytic reactions with recycling. In competitive autocatalytic reactions, species B and C both undergo an autocatalytic reaction with species A such that A+B→2B and A+C→2C. Small amounts of initially spatially localized B and C and a large amount of spatially homogeneous A are advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that local finite-time Lyapunov exponents (FTLEs) can accurately predict the final average concentrations of B and C after the reaction completes. The species that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If B and C start in regions with similar FTLEs, their average concentrations at the end of the reaction will also be similar. When a recycling reaction is added, the system evolves towards a single species state, with the FTLE often being useful in predicting which species fills the entire domain and which is depleted. The FTLE approach is also demonstrated for competitive autocatalytic reactions in journal bearing flow, an experimentally realizable flow that generates chaotic dynamics

  15. A coarse-grained model for the simulations of biomolecular interactions in cellular environments

    International Nuclear Information System (INIS)

    Xie, Zhong-Ru; Chen, Jiawen; Wu, Yinghao

    2014-01-01

    The interactions of bio-molecules constitute the key steps of cellular functions. However, in vivo binding properties differ significantly from their in vitro measurements due to the heterogeneity of cellular environments. Here we introduce a coarse-grained model based on rigid-body representation to study how factors such as cellular crowding and membrane confinement affect molecular binding. The macroscopic parameters such as the equilibrium constant and the kinetic rate constant are calibrated by adjusting the microscopic coefficients used in the numerical simulations. By changing these model parameters that are experimentally approachable, we are able to study the kinetic and thermodynamic properties of molecular binding, as well as the effects caused by specific cellular environments. We investigate the volumetric effects of crowded intracellular space on bio-molecular diffusion and diffusion-limited reactions. Furthermore, the binding constants of membrane proteins are currently difficult to measure. We provide quantitative estimations about how the binding of membrane proteins deviates from soluble proteins under different degrees of membrane confinements. The simulation results provide biological insights to the functions of membrane receptors on cell surfaces. Overall, our studies establish a connection between the details of molecular interactions and the heterogeneity of cellular environments

  16. Global asymptotic stability of bistable traveling fronts in reaction-diffusion systems and their applications to biological models

    International Nuclear Information System (INIS)

    Wu Shiliang; Li Wantong

    2009-01-01

    This paper deals with the global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts in a class of reaction-diffusion systems. The known results do not apply in solving these problems because the reaction terms do not satisfy the required monotone condition. To overcome the difficulty, a weak monotone condition is proposed for the reaction terms, which is called interval monotone condition. Under such a weak monotone condition, the existence and comparison theorem of solutions is first established for reaction-diffusion systems on R by appealing to the theory of abstract differential equations. The global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts are then proved by the elementary super- and sub-solution comparison and squeezing methods for nonlinear evolution equations. Finally, these abstract results are applied to a two species competition-diffusion model and a system modeling man-environment-man epidemics.

  17. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Science.gov (United States)

    Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

    2017-07-01

    This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  18. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Directory of Open Access Journals (Sweden)

    Shahid Hasnain

    2017-07-01

    Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  19. On Medium Chemical Reaction in Diffusion-Based Molecular Communication: a Two-Way Relaying Example

    OpenAIRE

    Farahnak-Ghazani, Maryam; Aminian, Gholamali; Mirmohseni, Mahtab; Gohari, Amin; Nasiri-Kenari, Masoumeh

    2016-01-01

    Chemical reactions are a prominent feature of molecular communication (MC) systems, with no direct parallels in wireless communications. While chemical reactions may be used inside the transmitter nodes, receiver nodes or the communication medium, we focus on its utility in the medium in this paper. Such chemical reactions can be used to perform computation over the medium as molecules diffuse and react with each other (physical-layer computation). We propose the use of chemical reactions for...

  20. Critical behavior in reaction-diffusion systems exhibiting absorbing phase transition

    CERN Document Server

    Ódor, G

    2003-01-01

    Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field approximation and simulations are given which support novel kind of non-equilibrium criticality. These are in contradiction with the implications of a suggested phenomenological, multiplicative noise Langevin equation approach and with some of recent numerical analysis. Simulation results for the one and two dimensional binary spreading 2A -> 4A, 4A -> 2A model display a new type of mean-field criticality characterized by alpha=1/3 and beta=1/2 critical exponents suggested in cond-mat/0210615.

  1. Rigorous Multicomponent Reactive Separations Modelling: Complete Consideration of Reaction-Diffusion Phenomena

    International Nuclear Information System (INIS)

    Ahmadi, A.; Meyer, M.; Rouzineau, D.; Prevost, M.; Alix, P.; Laloue, N.

    2010-01-01

    This paper gives the first step of the development of a rigorous multicomponent reactive separation model. Such a model is highly essential to further the optimization of acid gases removal plants (CO 2 capture, gas treating, etc.) in terms of size and energy consumption, since chemical solvents are conventionally used. Firstly, two main modelling approaches are presented: the equilibrium-based and the rate-based approaches. Secondly, an extended rate-based model with rigorous modelling methodology for diffusion-reaction phenomena is proposed. The film theory and the generalized Maxwell-Stefan equations are used in order to characterize multicomponent interactions. The complete chain of chemical reactions is taken into account. The reactions can be kinetically controlled or at chemical equilibrium, and they are considered for both liquid film and liquid bulk. Thirdly, the method of numerical resolution is described. Coupling the generalized Maxwell-Stefan equations with chemical equilibrium equations leads to a highly non-linear Differential-Algebraic Equations system known as DAE index 3. The set of equations is discretized with finite-differences as its integration by Gear method is complex. The resulting algebraic system is resolved by the Newton- Raphson method. Finally, the present model and the associated methods of numerical resolution are validated for the example of esterification of methanol. This archetype non-electrolytic system permits an interesting analysis of reaction impact on mass transfer, especially near the phase interface. The numerical resolution of the model by Newton-Raphson method gives good results in terms of calculation time and convergence. The simulations show that the impact of reactions at chemical equilibrium and that of kinetically controlled reactions with high kinetics on mass transfer is relatively similar. Moreover, the Fick's law is less adapted for multicomponent mixtures where some abnormalities such as counter-diffusion

  2. Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion

    KAUST Repository

    Carrillo, J. A.; Desvillettes, L.; Fellner, K.

    2009-01-01

    Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.

  3. Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion

    KAUST Repository

    Carrillo, J. A.

    2009-10-30

    Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.

  4. Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

    Science.gov (United States)

    Hu, Wenjie; Duan, Yueliang

    2018-04-01

    We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.

  5. A cellular automaton simulation of contaminant transport in porous media

    International Nuclear Information System (INIS)

    Freed, D.M.; Simonson, S.A.

    1995-01-01

    A simulation tool to investigate radionuclide transport in porous groundwater flow is described. The flow systems of interest are those important in determining the fate of radionuclides emplaced in an underground repository, such as saturated matrix flow, matrix and fracture flow in the unsaturated zone, and viscous fingering in porous fractures. The work discussed here is confined to consideration of saturated flow in porous media carrying a dilute, sorptive species. The simulation technique is based on a special class of cellular automata known as lattice gas automata (LGA) which are capable of predicting hydrodynamic behavior. The original two-dimensional scheme (that of Frisch et. al. known as the FHP model) used particles of unit mass traveling on a triangular lattice with unit velocity and undergoing simple collisions which conserve mass and momentum at each node. These microscopic rules go over to the incompressible Navier-Stokes equations in the macroscopic limit. One of the strengths of this technique is the natural way that heterogeneities, such as boundaries, are accommodated. Complex geometries such as those associated with porous microstructures can be modeled effectively. Several constructions based on the FHP model have been devised, including techniques to eliminate statistical noise, extension to three dimensions, and the addition of surface tension which leads to multiphase flow

  6. Critical regimes driven by recurrent mobility patterns of reaction-diffusion processes in networks

    Science.gov (United States)

    Gómez-Gardeñes, J.; Soriano-Paños, D.; Arenas, A.

    2018-04-01

    Reaction-diffusion processes1 have been widely used to study dynamical processes in epidemics2-4 and ecology5 in networked metapopulations. In the context of epidemics6, reaction processes are understood as contagions within each subpopulation (patch), while diffusion represents the mobility of individuals between patches. Recently, the characteristics of human mobility7, such as its recurrent nature, have been proven crucial to understand the phase transition to endemic epidemic states8,9. Here, by developing a framework able to cope with the elementary epidemic processes, the spatial distribution of populations and the commuting mobility patterns, we discover three different critical regimes of the epidemic incidence as a function of these parameters. Interestingly, we reveal a regime of the reaction-diffussion process in which, counter-intuitively, mobility is detrimental to the spread of disease. We analytically determine the precise conditions for the emergence of any of the three possible critical regimes in real and synthetic networks.

  7. Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

    Science.gov (United States)

    Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar

    2018-02-01

    We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

  8. A hybrid finite-element and cellular-automaton framework for modeling 3D microstructure of Ti–6Al–4V alloy during solid–solid phase transformation in additive manufacturing

    Science.gov (United States)

    Chen, Shaohua; Xu, Yaopengxiao; Jiao, Yang

    2018-06-01

    Additive manufacturing such as selective laser sintering and electron beam melting has become a popular technique which enables one to build near-net-shape product from packed powders. The performance and properties of the manufactured product strongly depends on its material microstructure, which is in turn determined by the processing conditions including beam power density, spot size, scanning speed and path etc. In this paper, we develop a computational framework that integrates the finite element method (FEM) and cellular automaton (CA) simulation to model the 3D microstructure of additively manufactured Ti–6Al–4V alloy, focusing on the β → α + β transition pathway in a consolidated alloy region as the power source moves away from this region. Specifically, the transient temperature field resulted from a scanning laser/electron beam following a zig-zag path is first obtained by solving nonlinear heat transfer equations using the FEM. Next, a CA model for the β → α + β phase transformation in the consolidated alloy is developed which explicitly takes into account the temperature dependent heterogeneous nucleation and anisotropic growth of α grains from the parent β phase field. We verify our model by reproducing the overall transition kinetics predicted by the Johnson–Mehl–Avrami–Kolmogorov theory under a typical processing condition and by quantitatively comparing our simulation results with available experimental data. The utility of the model is further demonstrated by generating large-field realistic 3D alloy microstructures for subsequent structure-sensitive micro-mechanical analysis. In addition, we employ our model to generate a wide spectrum of alloy microstructures corresponding to different processing conditions for establishing quantitative process-structure relations for the system.

  9. Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

    Science.gov (United States)

    Polyanin, A. D.; Sorokin, V. G.

    2017-12-01

    The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

  10. Existence and Asymptotic Stability of Periodic Solutions of the Reaction-Diffusion Equations in the Case of a Rapid Reaction

    Science.gov (United States)

    Nefedov, N. N.; Nikulin, E. I.

    2018-01-01

    A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal transition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated.

  11. Designing beauty the art of cellular automata

    CERN Document Server

    Martínez, Genaro

    2016-01-01

    This fascinating, colourful book offers in-depth insights and first-hand working experiences in the production of art works, using simple computational models with rich morphological behaviour, at the edge of mathematics, computer science, physics and biology. It organically combines ground breaking scientific discoveries in the theory of computation and complex systems with artistic representations of the research results. In this appealing book mathematicians, computer scientists, physicists, and engineers brought together marvelous and esoteric patterns generated by cellular automata, which are arrays of simple machines with complex behavior. Configurations produced by cellular automata uncover mechanics of dynamic patterns formation, their propagation and interaction in natural systems: heart pacemaker, bacterial membrane proteins, chemical rectors, water permeation in soil, compressed gas, cell division, population dynamics, reaction-diffusion media and self-organisation. The book inspires artists to tak...

  12. A percolation-like model for simulating inter-cellular diffusion in the context of bystander signalling in tumour

    International Nuclear Information System (INIS)

    Moulton, C.R.; Fleming, A.J.; Ebert, M.A.

    2011-01-01

    Full text: Despite ongoing active research, the role of the radiation bystander effect in modifying local tissue response to an ionising radiation dose remains unclear. The present study aims to provide new insight by simulating the diffusion-mediated inter-cellular communication processes in 2D and 3D cell-like structures to calculate likely signal ranges in the diffusion limited case. Random walks of individual signalling molecules were tracked between cells with inclusion of molecule-receptor interactions. The resulting diffusion anomaly is a function of cell density, signal uptake probability and the spatial arrangement of cells local to the signal origin. Uptake probability effects dominate percolation effects in disordered media. Diffu sion through 2D structures is more conducive to anomalous diffusion than diffusion through 3D structures. Values for time-dependent diffusion constants and permeability are derived for typical simulation parameters. Even at low signal uptake probabilities the communication range is restricted to a mean value of less than 100 foun owing to complete signal uptake by 600 s. This should be considered in light of the potential influence of signal relaying, flo dynamics or vasculature-mediated signalling.

  13. Reaction-assisted diffusion bonding of TiAl alloy to steel

    Energy Technology Data Exchange (ETDEWEB)

    Simões, S., E-mail: ssimoes@fe.up.pt [CEMUC, Department of Metallurgical and Materials Engineering, University of Porto, R. Dr. Roberto Frias, 4200-465 Porto (Portugal); Viana, F. [CEMUC, Department of Metallurgical and Materials Engineering, University of Porto, R. Dr. Roberto Frias, 4200-465 Porto (Portugal); Ramos, A.S.; Vieira, M.T. [CEMUC, Department of Mechanical Engineering, University of Coimbra, R. Luís Reis Santos, 3030-788 Coimbra (Portugal); Vieira, M.F. [CEMUC, Department of Metallurgical and Materials Engineering, University of Porto, R. Dr. Roberto Frias, 4200-465 Porto (Portugal)

    2016-03-01

    The dissimilar joining of TiAl to AISI 310 stainless steel by a reaction-assisted diffusion bonding process, using Ni/Al nanolayers as an interlayer, was investigated in the present work. The Ni and Al alternated nanolayers were deposited by d.c. magnetron sputtering onto the base materials, with a bilayer thickness of 14 nm. Joining experiments were performed at 800 °C for 60 min with compressive stress of 25 and 50 MPa. The effectiveness of the interlayer on the bonding process was assessed by microstructural characterization of the interface and by mechanical tests. Diffusion bonded joints were characterized by scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), high resolution transmission electron microscopy (HRTEM), scanning transmission electron microscopy (STEM) and analyzed by energy dispersive X-ray spectroscopy (EDS) in SEM and TEM and Fast Fourier Transform (FFT). The thickness of the interface region, together with its microstructural and mechanical characteristics, is affected by the use of Ni/Al multilayers; which promote joints with lower hardness values, closer to the values of the base materials, and exhibit higher shear strength. - Highlights: • Dissimilar joining by a reaction-assisted diffusion bonding were studied. • Ni/Al nanolayers allows join TiAl to steel in less demanding processing conditions. • The microstructural and mechanical characterization of the joints were investigated. • The fracture occurring in the TiAl base material attests to the sound joining. • Shear strength value decreases for joints with base materials without nanolayers.

  14. Parabolic equations in biology growth, reaction, movement and diffusion

    CERN Document Server

    Perthame, Benoît

    2015-01-01

    This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

  15. Pramana – Journal of Physics | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    A spreading to non-spreading transition is seen in the system. A cellular automaton version of the coupled system maps the spreading to non-spreading transition to a transition from a probabilistic to a deterministic cellular automaton. The solitonic sector of the system shows spatiotemporal intermittency with soliton creation, ...

  16. An Automaton Analysis of the Learning of a Miniature System of Japanese. Psychology Series.

    Science.gov (United States)

    Wexler, Kenneth Norman

    The purpose of the study reported here was to do an automata-theoretical and experimental investigation of the learning of the syntax and semantics of a second natural language. The main thrust of the work was to ask what kind of automaton a person can become. Various kinds of automata were considered, predictions were made from them, and these…

  17. Impulsive Synchronization of Reaction-Diffusion Neural Networks With Mixed Delays and Its Application to Image Encryption.

    Science.gov (United States)

    Chen, Wu-Hua; Luo, Shixian; Zheng, Wei Xing

    2016-12-01

    This paper presents a new impulsive synchronization criterion of two identical reaction-diffusion neural networks with discrete and unbounded distributed delays. The new criterion is established by applying an impulse-time-dependent Lyapunov functional combined with the use of a new type of integral inequality for treating the reaction-diffusion terms. The impulse-time-dependent feature of the proposed Lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction-diffusion neural networks than the conventional impulse-time-independent Lyapunov functions/functionals, while the new integral inequality, which is derived from Wirtinger's inequality, overcomes the conservatism introduced by the integral inequality used in the previous results. Numerical examples demonstrate the effectiveness of the proposed method. Later, the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image. The experimental results verify that the proposed image-encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks.

  18. Effects of chemical reaction on moving isothermal vertical plate with variable mass diffusion

    Directory of Open Access Journals (Sweden)

    Muthucumaraswamy R.

    2003-01-01

    Full Text Available An exact solution to the problem of flow past an impulsively started infinite vertical isothermal plate with variable mass diffusion is presented here, taking into account of the homogeneous chemical reaction of first-order. The dimensionless governing equations are solved by using the Laplace - transform technique. The velocity and skin-friction are studied for different parameters like chemical reaction parameter, Schmidt number and buoyancy ratio parameter. It is observed that the veloc­ity increases with decreasing chemical reaction parameter and increases with increasing buoyancy ratio parameter.

  19. Reaction probability derived from an interpolation formula for diffusion processes with an absorptive boundary condition

    International Nuclear Information System (INIS)

    Misawa, T.; Itakura, H.

    1995-01-01

    The present article focuses on a dynamical simulation of molecular motion in liquids. In the simulation involving diffusion-controlled reaction with discrete time steps, lack of information regarding the trajectory within the time step may result in a failure to count the number of reactions of the particles within the step. In order to rectify this, an interpolated diffusion process is used. The process is derived from a stochastic interpolation formula recently developed by the first author [J. Math. Phys. 34, 775 (1993)]. In this method, the probability that reaction has occurred during the time step given the initial and final positions of the particles is calculated. Some numerical examples confirm that the theoretical result corresponds to an improvement over the Clifford-Green work [Mol. Phys. 57, 123 (1986)] on the same matter

  20. Laser Spot Detection Based on Reaction Diffusion.

    Science.gov (United States)

    Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J M; Dormido, Raquel; Duro, Natividad

    2016-03-01

    Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.

  1. Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations

    Directory of Open Access Journals (Sweden)

    Guichen Lu

    2016-01-01

    Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.

  2. A reaction-diffusion model of ROS-induced ROS release in a mitochondrial network.

    Directory of Open Access Journals (Sweden)

    Lufang Zhou

    2010-01-01

    Full Text Available Loss of mitochondrial function is a fundamental determinant of cell injury and death. In heart cells under metabolic stress, we have previously described how the abrupt collapse or oscillation of the mitochondrial energy state is synchronized across the mitochondrial network by local interactions dependent upon reactive oxygen species (ROS. Here, we develop a mathematical model of ROS-induced ROS release (RIRR based on reaction-diffusion (RD-RIRR in one- and two-dimensional mitochondrial networks. The nodes of the RD-RIRR network are comprised of models of individual mitochondria that include a mechanism of ROS-dependent oscillation based on the interplay between ROS production, transport, and scavenging; and incorporating the tricarboxylic acid (TCA cycle, oxidative phosphorylation, and Ca(2+ handling. Local mitochondrial interaction is mediated by superoxide (O2.- diffusion and the O2.(--dependent activation of an inner membrane anion channel (IMAC. In a 2D network composed of 500 mitochondria, model simulations reveal DeltaPsi(m depolarization waves similar to those observed when isolated guinea pig cardiomyocytes are subjected to a localized laser-flash or antioxidant depletion. The sensitivity of the propagation rate of the depolarization wave to O(2.- diffusion, production, and scavenging in the reaction-diffusion model is similar to that observed experimentally. In addition, we present novel experimental evidence, obtained in permeabilized cardiomyocytes, confirming that DeltaPsi(m depolarization is mediated specifically by O2.-. The present work demonstrates that the observed emergent macroscopic properties of the mitochondrial network can be reproduced in a reaction-diffusion model of RIRR. Moreover, the findings have uncovered a novel aspect of the synchronization mechanism, which is that clusters of mitochondria that are oscillating can entrain mitochondria that would otherwise display stable dynamics. The work identifies the

  3. Modeling Studies of Inhomogeneity Effects during Laser Flash Photolysis Experiments: A Reaction-Diffusion Approach.

    Science.gov (United States)

    Dóka, Éva; Lente, Gábor

    2017-04-13

    This work presents a rigorous mathematical study of the effect of unavoidable inhomogeneities in laser flash photolysis experiments. There are two different kinds of inhomegenities: the first arises from diffusion, whereas the second one has geometric origins (the shapes of the excitation and detection light beams). Both of these are taken into account in our reported model, which gives rise to a set of reaction-diffusion type partial differential equations. These equations are solved by a specially developed finite volume method. As an example, the aqueous reaction between the sulfate ion radical and iodide ion is used, for which sufficiently detailed experimental data are available from an earlier publication. The results showed that diffusion itself is in general too slow to influence the kinetic curves on the usual time scales of laser flash photolysis experiments. However, the use of the absorbances measured (e.g., to calculate the molar absorption coefficients of transient species) requires very detailed mathematical consideration and full knowledge of the geometrical shapes of the excitation laser beam and the separate detection light beam. It is also noted that the usual pseudo-first-order approach to evaluating the kinetic traces can be used successfully even if the usual large excess condition is not rigorously met in the reaction cell locally.

  4. Multi-scale modeling of diffusion-controlled reactions in polymers: renormalisation of reactivity parameters.

    Science.gov (United States)

    Everaers, Ralf; Rosa, Angelo

    2012-01-07

    The quantitative description of polymeric systems requires hierarchical modeling schemes, which bridge the gap between the atomic scale, relevant to chemical or biomolecular reactions, and the macromolecular scale, where the longest relaxation modes occur. Here, we use the formalism for diffusion-controlled reactions in polymers developed by Wilemski, Fixman, and Doi to discuss the renormalisation of the reactivity parameters in polymer models with varying spatial resolution. In particular, we show that the adjustments are independent of chain length. As a consequence, it is possible to match reactions times between descriptions with different resolution for relatively short reference chains and to use the coarse-grained model to make quantitative predictions for longer chains. We illustrate our results by a detailed discussion of the classical problem of chain cyclization in the Rouse model, which offers the simplest example of a multi-scale descriptions, if we consider differently discretized Rouse models for the same physical system. Moreover, we are able to explore different combinations of compact and non-compact diffusion in the local and large-scale dynamics by varying the embedding dimension.

  5. Flexible single molecule simulation of reaction-diffusion processes

    International Nuclear Information System (INIS)

    Hellander, Stefan; Loetstedt, Per

    2011-01-01

    An algorithm is developed for simulation of the motion and reactions of single molecules at a microscopic level. The molecules diffuse in a solvent and react with each other or a polymer and molecules can dissociate. Such simulations are of interest e.g. in molecular biology. The algorithm is similar to the Green's function reaction dynamics (GFRD) algorithm by van Zon and ten Wolde where longer time steps can be taken by computing the probability density functions (PDFs) and then sample from the distribution functions. Our computation of the PDFs is much less complicated than GFRD and more flexible. The solution of the partial differential equation for the PDF is split into two steps to simplify the calculations. The sampling is without splitting error in two of the coordinate directions for a pair of molecules and a molecule-polymer interaction and is approximate in the third direction. The PDF is obtained either from an analytical solution or a numerical discretization. The errors due to the operator splitting, the partitioning of the system, and the numerical approximations are analyzed. The method is applied to three different systems involving up to four reactions. Comparisons with other mesoscopic and macroscopic models show excellent agreement.

  6. Reaction diffusion and solid state chemical kinetics handbook

    CERN Document Server

    Dybkov, V I

    2010-01-01

    This monograph deals with a physico-chemical approach to the problem of the solid-state growth of chemical compound layers and reaction-diffusion in binary heterogeneous systems formed by two solids; as well as a solid with a liquid or a gas. It is explained why the number of compound layers growing at the interface between the original phases is usually much lower than the number of chemical compounds in the phase diagram of a given binary system. For example, of the eight intermetallic compounds which exist in the aluminium-zirconium binary system, only ZrAl3 was found to grow as a separate

  7. Laser Spot Detection Based on Reaction Diffusion

    Directory of Open Access Journals (Sweden)

    Alejandro Vázquez-Otero

    2016-03-01

    Full Text Available Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.

  8. Mode-locking in advection-reaction-diffusion systems: An invariant manifold perspective

    Science.gov (United States)

    Locke, Rory A.; Mahoney, John R.; Mitchell, Kevin A.

    2018-01-01

    Fronts propagating in two-dimensional advection-reaction-diffusion systems exhibit a rich topological structure. When the underlying fluid flow is periodic in space and time, the reaction front can lock to the driving frequency. We explain this mode-locking phenomenon using the so-called burning invariant manifolds (BIMs). In fact, the mode-locked profile is delineated by a BIM attached to a relative periodic orbit (RPO) of the front element dynamics. Changes in the type (and loss) of mode-locking can be understood in terms of local and global bifurcations of the RPOs and their BIMs. We illustrate these concepts numerically using a chain of alternating vortices in a channel geometry.

  9. Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata

    Directory of Open Access Journals (Sweden)

    Nicolai Lang, Hans Peter Büchler

    2018-01-01

    Full Text Available Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the one-dimensional Majorana chain and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.

  10. Self-organisation in Cellular Automata with Coalescent Particles: Qualitative and Quantitative Approaches

    Science.gov (United States)

    Hellouin de Menibus, Benjamin; Sablik, Mathieu

    2017-06-01

    This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial configuration at random according to some initial shift-ergodic measure, and use the limit measure to describe the asymptotic behaviour of the automata. We first take a qualitative approach, i.e. we obtain information on the limit measure(s). We prove that only particles moving in one particular direction can persist asymptotically. This provides some previously unknown information on the limit measures of various deterministic and probabilistic cellular automata: 3 and 4-cyclic cellular automata [introduced by Fisch (J Theor Probab 3(2):311-338, 1990; Phys D 45(1-3):19-25, 1990)], one-sided captive cellular automata [introduced by Theyssier (Captive Cellular Automata, 2004)], the majority-traffic cellular automaton, a self stabilisation process towards a discrete line [introduced by Regnault and Rémila (in: Mathematical Foundations of Computer Science 2015—40th International Symposium, MFCS 2015, Milan, Italy, Proceedings, Part I, 2015)]. In a second time we restrict our study to a subclass, the gliders cellular automata. For this class we show quantitative results, consisting in the asymptotic law of some parameters: the entry times [generalising K ůrka et al. (in: Proceedings of AUTOMATA, 2011)], the density of particles and the rate of convergence to the limit measure.

  11. Quantitative modeling of the reaction/diffusion kinetics of two-chemistry photopolymers

    Science.gov (United States)

    Kowalski, Benjamin Andrew

    Optically driven diffusion in photopolymers is an appealing material platform for a broad range of applications, in which the recorded refractive index patterns serve either as images (e.g. data storage, display holography) or as optical elements (e.g. custom GRIN components, integrated optical devices). A quantitative understanding of the reaction/diffusion kinetics is difficult to obtain directly, but is nevertheless necessary in order to fully exploit the wide array of design freedoms in these materials. A general strategy for characterizing these kinetics is proposed, in which key processes are decoupled and independently measured. This strategy enables prediction of a material's potential refractive index change, solely on the basis of its chemical components. The degree to which a material does not reach this potential reveals the fraction of monomer that has participated in unwanted reactions, reducing spatial resolution and dynamic range. This approach is demonstrated for a model material similar to commercial media, achieving quantitative predictions of index response over three orders of exposure dose (~1 to ~103 mJ cm-2) and three orders of feature size (0.35 to 500 microns). The resulting insights enable guided, rational design of new material formulations with demonstrated performance improvement.

  12. Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models

    Directory of Open Access Journals (Sweden)

    Narcisa Apreutesei

    2014-05-01

    Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.

  13. Solid state reaction studies in Fe3O4–TiO2 system by diffusion couple method

    International Nuclear Information System (INIS)

    Ren, Zhongshan; Hu, Xiaojun; Xue, Xiangxin; Chou, Kuochih

    2013-01-01

    Highlights: •The solid state reactions of Fe2O3-TiO2 system was studied by the diffusion couple method. •Different products were formed by diffusion, and the FeTiO3 was more stable phase. •The inter-diffusion coefficients and diffusion activation energy were estimated. -- Abstract: The solid state reactions in Fe 3 O 4 –TiO 2 system has been studied by diffusion couple experiments at 1323–1473 K, in which the oxygen partial pressure was controlled by the CO–CO 2 gas mixture. The XRD analysis was used to confirm the phases of the inter-compound, and the concentration profiles were determined by electron probe microanalysis (EPMA). Based on the concentration profile of Ti, the inter-diffusion coefficients in Fe 3 O 4 phase, which were both temperature and concentration of Ti ions dependent, were calculated by the modified Boltzmann–Matano method. According to the relation between the thickness of diffusion layer and temperature, the diffusion coefficient of the Fe 3 O 4 –TiO 2 system was obtained. According to the Arrhenius equation, the estimated diffusion activation energy was about 282.1 ± 18.8 kJ mol −1

  14. Hopf bifurcation in a reaction-diffusive two-species model with nonlocal delay effect and general functional response

    International Nuclear Information System (INIS)

    Han, Renji; Dai, Binxiang

    2017-01-01

    Highlights: • We model general two-dimensional reaction-diffusion with nonlocal delay. • The existence of unique positive steady state is studied. • The bilinear form for the proposed system is given. • The existence, direction of Hopf bifurcation are given by symmetry method. - Abstract: A nonlocal delayed reaction-diffusive two-species model with Dirichlet boundary condition and general functional response is investigated in this paper. Based on the Lyapunov–Schmidt reduction, the existence, bifurcation direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady-state solution are obtained, where the time delay is taken as the bifurcation parameter. Moreover, the general results are applied to a diffusive Lotka–Volterra type food-limited population model with nonlocal delay effect, and it is found that diffusion and nonlocal delay can also affect the other dynamic behavior of the system by numerical experiments.

  15. Synchronous parallel kinetic Monte Carlo for continuum diffusion-reaction systems

    International Nuclear Information System (INIS)

    Martinez, E.; Marian, J.; Kalos, M.H.; Perlado, J.M.

    2008-01-01

    A novel parallel kinetic Monte Carlo (kMC) algorithm formulated on the basis of perfect time synchronicity is presented. The algorithm is intended as a generalization of the standard n-fold kMC method, and is trivially implemented in parallel architectures. In its present form, the algorithm is not rigorous in the sense that boundary conflicts are ignored. We demonstrate, however, that, in their absence, or if they were correctly accounted for, our algorithm solves the same master equation as the serial method. We test the validity and parallel performance of the method by solving several pure diffusion problems (i.e. with no particle interactions) with known analytical solution. We also study diffusion-reaction systems with known asymptotic behavior and find that, for large systems with interaction radii smaller than the typical diffusion length, boundary conflicts are negligible and do not affect the global kinetic evolution, which is seen to agree with the expected analytical behavior. Our method is a controlled approximation in the sense that the error incurred by ignoring boundary conflicts can be quantified intrinsically, during the course of a simulation, and decreased arbitrarily (controlled) by modifying a few problem-dependent simulation parameters

  16. Step-by-Step Simulation of Radiation Chemistry Using Green Functions for Diffusion-Influenced Reactions

    Science.gov (United States)

    Plante, Ianik; Cucinotta, Francis A.

    2011-01-01

    Radiolytic species are formed approximately 1 ps after the passage of ionizing radiation through matter. After their formation, they diffuse and chemically react with other radiolytic species and neighboring biological molecules, leading to various oxidative damage. Therefore, the simulation of radiation chemistry is of considerable importance to understand how radiolytic species damage biological molecules [1]. The step-by-step simulation of chemical reactions is difficult, because the radiolytic species are distributed non-homogeneously in the medium. Consequently, computational approaches based on Green functions for diffusion-influenced reactions should be used [2]. Recently, Green functions for more complex type of reactions have been published [3-4]. We have developed exact random variate generators of these Green functions [5], which will allow us to use them in radiation chemistry codes. Moreover, simulating chemistry using the Green functions is which is computationally very demanding, because the probabilities of reactions between each pair of particles should be evaluated at each timestep [2]. This kind of problem is well adapted for General Purpose Graphic Processing Units (GPGPU), which can handle a large number of similar calculations simultaneously. These new developments will allow us to include more complex reactions in chemistry codes, and to improve the calculation time. This code should be of importance to link radiation track structure simulations and DNA damage models.

  17. Hybrid approaches for multiple-species stochastic reaction-diffusion models

    Science.gov (United States)

    Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

    2015-10-01

    Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

  18. Hybrid approaches for multiple-species stochastic reaction-diffusion models.

    KAUST Repository

    Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen

    2015-01-01

    Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

  19. Hybrid approaches for multiple-species stochastic reaction-diffusion models.

    KAUST Repository

    Spill, Fabian

    2015-10-01

    Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

  20. Cellular automata and integrodifferential equation models for cell renewal in mosaic tissues

    Science.gov (United States)

    Bloomfield, J. M.; Sherratt, J. A.; Painter, K. J.; Landini, G.

    2010-01-01

    Mosaic tissues are composed of two or more genetically distinct cell types. They occur naturally, and are also a useful experimental method for exploring tissue growth and maintenance. By marking the different cell types, one can study the patterns formed by proliferation, renewal and migration. Here, we present mathematical modelling suggesting that small changes in the type of interaction that cells have with their local cellular environment can lead to very different outcomes for the composition of mosaics. In cell renewal, proliferation of each cell type may depend linearly or nonlinearly on the local proportion of cells of that type, and these two possibilities produce very different patterns. We study two variations of a cellular automaton model based on simple rules for renewal. We then propose an integrodifferential equation model, and again consider two different forms of cellular interaction. The results of the continuous and cellular automata models are qualitatively the same, and we observe that changes in local environment interaction affect the dynamics for both. Furthermore, we demonstrate that the models reproduce some of the patterns seen in actual mosaic tissues. In particular, our results suggest that the differing patterns seen in organ parenchymas may be driven purely by the process of cell replacement under different interaction scenarios. PMID:20375040

  1. Dynamical Behaviors of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays

    Directory of Open Access Journals (Sweden)

    Li Wan

    2012-01-01

    Full Text Available This paper investigates dynamical behaviors of stochastic Cohen-Grossberg neural network with delays and reaction diffusion. By employing Lyapunov method, Poincaré inequality and matrix technique, some sufficient criteria on ultimate boundedness, weak attractor, and asymptotic stability are obtained. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

  2. Degree, instability and bifurcation of reaction-diffusion systems with obstacles near certain hyperbolas

    Czech Academy of Sciences Publication Activity Database

    Eisner, J.; Väth, Martin

    2016-01-01

    Roč. 135, April (2016), s. 158-193 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : reaction-diffusion system * turing instability * global bifurcation Subject RIV: BA - General Mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X16000146

  3. Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors

    International Nuclear Information System (INIS)

    Ivanov, Konstantin L.; Lukzen, Nikita N.; Sadovsky, Vladimir M.

    2015-01-01

    In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical “microreactor,” i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the “pole” of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting

  4. Characterization of the reaction layer in U-7wt%Mo/Al diffusion couples

    Energy Technology Data Exchange (ETDEWEB)

    Mirandou, M.I.; Balart, S.N.; Ortiz, M.; Granovsky, M.S. E-mail: granovsk@cnea.gov.ar

    2003-11-15

    The reaction layer in chemical diffusion couples U-7wt%Mo/Al was investigated using optical and scanning electron microscopy, electron probe microanalysis and X-ray diffraction (XRD) techniques. When the U-7wt%Mo alloy was previously homogenized and the {gamma}(U, Mo) phase was retained, the formation of (U, Mo)Al{sub 3} and (U, Mo)Al{sub 4} was observed at 580 deg. C. Also a very thin band was detected close to the Al side, the structure of the ternary compound Al{sub 20}UMo{sub 2} might be assigned to it. When the decomposition of the {gamma}(U, Mo) took place, a drastic change in the diffusion behavior was observed. In this case, XRD indicated the presence of phases with the structures of (U, Mo)Al{sub 3}, Al{sub 43}U{sub 6}Mo{sub 4}, {gamma}(U, Mo) and {alpha}(U) in the reaction layer.

  5. Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction

    Science.gov (United States)

    Tuan, Nguyen Huy; Van Au, Vo; Khoa, Vo Anh; Lesnic, Daniel

    2017-05-01

    The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.

  6. Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

    Science.gov (United States)

    Owolabi, Kolade M.

    2018-03-01

    In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

  7. An extension to Galilean relativity gives rise to quantum mechanics framework

    Science.gov (United States)

    Berkovich, Simon

    The presented scheme for quantum mechanics appeared from considering Cellular Automaton Universe in view of the hidden energy associated with the property of inertia. Galilean relativity states that all inertial frames are equivalent. Our consideration reveals one seemingly small exception - the original frame of reference for the material formations of the Cellular Automaton infrastructure is not isotropic. This frame of reference has a distinctive direction as long as elementary particles of matter are generated by cellular automaton relocations As a result, Cellular Automaton Universe basically complying with the laws of macrophysics for bulk bodies, could exhibit peculiar characteristics for microphysics.. Why the states of microobjects are described by complex numbers is obscure. The observables are presented by real numbers through corresponding macro manipulations. In the inertial frame with unidirectional anisotropy isolated particles are characterized by two numbers; magnitude of their velocity and inclination angle to motion direction. So, these quantum states are mapped to a complex Hilbert space with zero vector representing bulk bodies. The effect of spin may be associated with the sign of the inclination angle trending separations for Stern-Gerlach output and Paul Principle. Emeritus.

  8. Modeling evolution and immune system by cellular automata

    International Nuclear Information System (INIS)

    Bezzi, M.

    2001-01-01

    In this review the behavior of two different biological systems is investigated using cellular automata. Starting from this spatially extended approach it is also tried, in some cases, to reduce the complexity of the system introducing mean-field approximation, and solving (or trying to solve) these simplified systems. It is discussed the biological meaning of the results, the comparison with experimental data (if available) and the different features between spatially extended and mean-field versions. The biological systems considered in this review are the following: Darwinian evolution in simple ecosystems and immune system response. In the first section the main features of molecular evolution are introduced, giving a short survey of genetics for physicists and discussing some models for prebiotic systems and simple ecosystems. It is also introduced a cellular automaton model for studying a set of evolving individuals in a general fitness landscape, considering also the effects of co-evolution. In particular the process of species formation (speciation) is described in sect. 5. The second part deals with immune system modeling. The biological features of immune response are discussed, as well as it is introduced the concept of shape space and of idiotypic network. More detailed reviews which deal with immune system models (mainly focused on idiotypic network models) can be found. Other themes here discussed: the applications of CA to immune system modeling, two complex cellular automata for humoral and cellular immune response. Finally, it is discussed the biological data and the general conclusions are drawn in the last section

  9. Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources

    Directory of Open Access Journals (Sweden)

    Ida de Bonis

    2017-09-01

    Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.

  10. Passing to the limit in a Wasserstein gradient flow : from diffusion to reaction

    NARCIS (Netherlands)

    Arnrich, S.; Mielke, A.; Peletier, M.A.; Savaré, G.; Veneroni, M.

    2012-01-01

    We study a singular-limit problem arising in the modelling of chemical reactions. At finite e > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1 / e and in the limit e --> 0, the solution concentrates

  11. Modeling the Influence of Diffusion-Controlled Reactions and Residual Termination and Deactivation on the Rate and Control of Bulk ATRP at High Conversions

    Directory of Open Access Journals (Sweden)

    Ali Mohammad Rabea

    2015-04-01

    Full Text Available In high-conversion atom transfer radical polymerization (ATRP, all the reactions, such as radical termination, radical deactivation, dormant chain activation, monomer propagation, etc. could become diffusion controlled sooner or later, depending on relative diffusivities of the involved reacting species. These diffusion-controlled reactions directly affect the rate of polymerization and the control of polymer molecular weight. A model is developed to investigate the influence of diffusion-controlled reactions on the high conversion ATRP kinetics. Model simulation reveals that diffusion-controlled termination slightly increases the rate, but it is the diffusion-controlled deactivation that causes auto-acceleration in the rate (“gel effect” and loss of control. At high conversions, radical chains are “trapped” because of high molecular weight. However, radical centers can still migrate through (1 radical deactivation–activation cycles and (2 monomer propagation, which introduce “residual termination” reactions. It is found that the “residual termination” does not have much influence on the polymerization kinetics. The migration of radical centers through propagation can however facilitate catalytic deactivation of radicals, which improves the control of polymer molecular weight to some extent. Dormant chain activation and monomer propagation also become diffusion controlled and finally stop the polymerization when the system approaches its glass state.

  12. On one model problem for the reaction-diffusion-advection equation

    Science.gov (United States)

    Davydova, M. A.; Zakharova, S. A.; Levashova, N. T.

    2017-09-01

    The asymptotic behavior of the solution with boundary layers in the time-independent mathematical model of reaction-diffusion-advection arising when describing the distribution of greenhouse gases in the surface atmospheric layer is studied. On the basis of the asymptotic method of differential inequalities, the existence of a boundary-layer solution and its asymptotic Lyapunov stability as a steady-state solution of the corresponding parabolic problem is proven. One of the results of this work is the determination of the local domain of the attraction of a boundary-layer solution.

  13. Doubly Periodic Traveling Waves in a Cellular Neural Network with Linear Reaction

    Directory of Open Access Journals (Sweden)

    Lin JianJhong

    2009-01-01

    Full Text Available Szekeley observed that the dynamic pattern of the locomotion of salamanders can be explained by periodic vector sequences generated by logical neural networks. Such sequences can mathematically be described by "doubly periodic traveling waves" and therefore it is of interest to propose dynamic models that may produce such waves. One such dynamic network model is built here based on reaction-diffusion principles and a complete discussion is given for the existence of doubly periodic waves as outputs. Since there are 2 parameters in our model and 4 a priori unknown parameters involved in our search of solutions, our results are nontrivial. The reaction term in our model is a linear function and hence our results can also be interpreted as existence criteria for solutions of a nontrivial linear problem depending on 6 parameters.

  14. Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method

    International Nuclear Information System (INIS)

    Mittal, R.C.; Rohila, Rajni

    2016-01-01

    In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.

  15. A diffusion-limited reaction model for self-propagating Al/Pt multilayers with quench limits

    Science.gov (United States)

    Kittell, D. E.; Yarrington, C. D.; Hobbs, M. L.; Abere, M. J.; Adams, D. P.

    2018-04-01

    A diffusion-limited reaction model was calibrated for Al/Pt multilayers ignited on oxidized silicon, sapphire, and tungsten substrates, as well as for some Al/Pt multilayers ignited as free-standing foils. The model was implemented in a finite element analysis code and used to match experimental burn front velocity data collected from several years of testing at Sandia National Laboratories. Moreover, both the simulations and experiments reveal well-defined quench limits in the total Al + Pt layer (i.e., bilayer) thickness. At these limits, the heat generated from atomic diffusion is insufficient to support a self-propagating wave front on top of the substrates. Quench limits for reactive multilayers are seldom reported and are found to depend on the thermal properties of the individual layers. Here, the diffusion-limited reaction model is generalized to allow for temperature- and composition-dependent material properties, phase change, and anisotropic thermal conductivity. Utilizing this increase in model fidelity, excellent overall agreement is shown between the simulations and experimental results with a single calibrated parameter set. However, the burn front velocities of Al/Pt multilayers ignited on tungsten substrates are over-predicted. Possible sources of error are discussed and a higher activation energy (from 41.9 kJ/mol.at. to 47.5 kJ/mol.at.) is shown to bring the simulations into agreement with the velocity data observed on tungsten substrates. This higher activation energy suggests an inhibited diffusion mechanism present at lower heating rates.

  16. Allergic Contact Dermatitis with Diffuse Erythematous Reaction from Diisopropanolamine in a Compress

    Directory of Open Access Journals (Sweden)

    Tomoko Rind

    2010-04-01

    Full Text Available Compresses containing a nonsteroidal antiinflammatory drug (NSAID are commonly used in Japan. However, this treatment may induce both allergic and photoallergic contact dermatitis from the NSAIDs and their ingredients. Here, we describe a case of allergic contact dermatitis with diffuse erythematous reaction due to diisopropanolamine in the applied compress. The absorption of diisopropanolamine might have been enhanced by the occlusive condition.

  17. High Severity Wildfire Effect On Rainfall Infiltration And Runoff: A Cellular Automata Based Simulation

    Science.gov (United States)

    Vergara-Blanco, J. E.; Leboeuf-Pasquier, J.; Benavides-Solorio, J. D. D.

    2017-12-01

    A simulation software that reproduces rainfall infiltration and runoff for a storm event in a particular forest area is presented. A cellular automaton is utilized to represent space and time. On the time scale, the simulation is composed by a sequence of discrete time steps. On the space scale, the simulation is composed of forest surface cells. The software takes into consideration rain intensity and length, individual forest cell soil absorption capacity evolution, and surface angle of inclination. The software is developed with the C++ programming language. The simulation is executed on a 100 ha area within La Primavera Forest in Jalisco, Mexico. Real soil texture for unburned terrain and high severity wildfire affected terrain is employed to recreate the specific infiltration profile. Historical rainfall data of a 92 minute event is used. The Horton infiltration equation is utilized for infiltration capacity calculation. A Digital Elevation Model (DEM) is employed to reproduce the surface topography. The DEM is displayed with a 3D mesh graph where individual surface cells can be observed. The plot colouring renders water content development at the cell level throughout the storm event. The simulation shows that the cumulative infiltration and runoff which take place at the surface cell level depend on the specific storm intensity, fluctuation and length, overall terrain topography, cell slope, and soil texture. Rainfall cumulative infiltration for unburned and high severity wildfire terrain are compared: unburned terrain exhibits a significantly higher amount of rainfall infiltration.It is concluded that a cellular automaton can be utilized with a C++ program to reproduce rainfall infiltration and runoff under diverse soil texture, topographic and rainfall conditions in a forest setting. This simulation is geared for an optimization program to pinpoint the locations of a series of forest land remediation efforts to support reforestation or to minimize runoff.

  18. Confining Domains Lead to Reaction Bursts: Reaction Kinetics in the Plasma Membrane

    Science.gov (United States)

    Kalay, Ziya; Fujiwara, Takahiro K.; Kusumi, Akihiro

    2012-01-01

    Confinement of molecules in specific small volumes and areas within a cell is likely to be a general strategy that is developed during evolution for regulating the interactions and functions of biomolecules. The cellular plasma membrane, which is the outermost membrane that surrounds the entire cell, was considered to be a continuous two-dimensional liquid, but it is becoming clear that it consists of numerous nano-meso-scale domains with various lifetimes, such as raft domains and cytoskeleton-induced compartments, and membrane molecules are dynamically trapped in these domains. In this article, we give a theoretical account on the effects of molecular confinement on reversible bimolecular reactions in a partitioned surface such as the plasma membrane. By performing simulations based on a lattice-based model of diffusion and reaction, we found that in the presence of membrane partitioning, bimolecular reactions that occur in each compartment proceed in bursts during which the reaction rate is sharply and briefly increased even though the asymptotic reaction rate remains the same. We characterized the time between reaction bursts and the burst amplitude as a function of the model parameters, and discussed the biological significance of the reaction bursts in the presence of strong inhibitor activity. PMID:22479350

  19. Confining domains lead to reaction bursts: reaction kinetics in the plasma membrane.

    Directory of Open Access Journals (Sweden)

    Ziya Kalay

    Full Text Available Confinement of molecules in specific small volumes and areas within a cell is likely to be a general strategy that is developed during evolution for regulating the interactions and functions of biomolecules. The cellular plasma membrane, which is the outermost membrane that surrounds the entire cell, was considered to be a continuous two-dimensional liquid, but it is becoming clear that it consists of numerous nano-meso-scale domains with various lifetimes, such as raft domains and cytoskeleton-induced compartments, and membrane molecules are dynamically trapped in these domains. In this article, we give a theoretical account on the effects of molecular confinement on reversible bimolecular reactions in a partitioned surface such as the plasma membrane. By performing simulations based on a lattice-based model of diffusion and reaction, we found that in the presence of membrane partitioning, bimolecular reactions that occur in each compartment proceed in bursts during which the reaction rate is sharply and briefly increased even though the asymptotic reaction rate remains the same. We characterized the time between reaction bursts and the burst amplitude as a function of the model parameters, and discussed the biological significance of the reaction bursts in the presence of strong inhibitor activity.

  20. Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics

    KAUST Repository

    Franz, Benjamin

    2013-06-19

    Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.

  1. Investigation of high burnup structures in uranium dioxide applying cellular automata: algorithms and codes

    International Nuclear Information System (INIS)

    Akishina, E.P.; Kostenko, B.F.; Ivanov, V.V.

    2003-01-01

    A new method of research in spatial structures that result from uranium dioxide burning in nuclear reactors of modern atomic plants is suggested. The method is based on the presentation of images of the mentioned structures in the form of the working field of a cellular automaton (CA). First, it has allowed one to extract some important quantitative characteristics of the structures directly from the micrographs of the uranium fuel surface. Secondly, the CA has been found out to allow one to formulate easily the dynamics of the evolution of the studied structures in terms of such micrograph elements as spots, spots' boundaries, cracks, etc. Relation has been found between the dynamics and some exactly solvable models of the theory of cellular automata, in particular, the Ising model and the vote model. This investigation gives a detailed description of some CA algorithms which allow one to perform the fuel surface image processing and to model its evolution caused by burnup or chemical etching. (author)

  2. Ionic Diffusion and Kinetic Homogeneous Chemical Reactions in the Pore Solution of Porous Materials with Moisture Transport

    DEFF Research Database (Denmark)

    Johannesson, Björn

    2009-01-01

    Results from a systematic continuum mixture theory will be used to establish the governing equations for ionic diffusion and chemical reactions in the pore solution of a porous material subjected to moisture transport. The theory in use is the hybrid mixture theory (HMT), which in its general form......’s law of diffusion and the generalized Darcy’s law will be used together with derived constitutive equations for chemical reactions within phases. The mass balance equations for the constituents and the phases together with the constitutive equations gives the coupled set of non-linear differential...... general description of chemical reactions among constituents is described. The Petrov – Galerkin approach are used in favour of the standard Galerkin weighting in order to improve the solution when the convective part of the problem is dominant. A modified type of Newton – Raphson scheme is derived...

  3. Convergence to a pulsating travelling wave for an epidemic reaction-diffusion system with non-diffusive susceptible population.

    Science.gov (United States)

    Ducrot, Arnaud; Giletti, Thomas

    2014-09-01

    In this work we study the asymptotic behaviour of the Kermack-McKendrick reaction-diffusion system in a periodic environment with non-diffusive susceptible population. This problem was proposed by Kallen et al. as a model for the spatial spread for epidemics, where it can be reasonable to assume that the susceptible population is motionless. For arbitrary dimensional space we prove that large classes of solutions of such a system have an asymptotic spreading speed in large time, and that the infected population has some pulse-like asymptotic shape. The analysis of the one-dimensional problem is more developed, as we are able to uncover a much more accurate description of the profile of solutions. Indeed, we will see that, for some initially compactly supported infected population, the profile of the solution converges to some pulsating travelling wave with minimal speed, that is to some entire solution moving at a constant positive speed and whose profile's shape is periodic in time.

  4. Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics

    International Nuclear Information System (INIS)

    Windus, Alastair; Jensen, Henrik J

    2008-01-01

    We consider a reaction-diffusion model incorporating the reactions A→φ, A→2A and 2A→3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. While we comment on this critical behaviour, the main focus of the paper is on the geometry of the population clusters that form. We observe the different cluster structures that arise at criticality for the three different types of critical behaviour and show that there exists a linear relationship for the survival probability against initial cluster size at the tricritical point only.

  5. The Influence of Receptor-Mediated Interactions on Reaction-Diffusion Mechanisms of Cellular Self-organisation

    KAUST Repository

    Klika, Václav

    2011-11-10

    Understanding the mechanisms governing and regulating self-organisation in the developing embryo is a key challenge that has puzzled and fascinated scientists for decades. Since its conception in 1952 the Turing model has been a paradigm for pattern formation, motivating numerous theoretical and experimental studies, though its verification at the molecular level in biological systems has remained elusive. In this work, we consider the influence of receptor-mediated dynamics within the framework of Turing models, showing how non-diffusing species impact the conditions for the emergence of self-organisation. We illustrate our results within the framework of hair follicle pre-patterning, showing how receptor interaction structures can be constrained by the requirement for patterning, without the need for detailed knowledge of the network dynamics. Finally, in the light of our results, we discuss the ability of such systems to pattern outside the classical limits of the Turing model, and the inherent dangers involved in model reduction. © 2011 Society for Mathematical Biology.

  6. Square Turing patterns in reaction-diffusion systems with coupled layers

    Energy Technology Data Exchange (ETDEWEB)

    Li, Jing [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Wang, Hongli, E-mail: hlwang@pku.edu.cn, E-mail: qi@pku.edu.cn [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Center for Quantitative Biology, Peking University, Beijing 100871 (China); Ouyang, Qi, E-mail: hlwang@pku.edu.cn, E-mail: qi@pku.edu.cn [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Center for Quantitative Biology, Peking University, Beijing 100871 (China); The Peking-Tsinghua Center for Life Sciences, Beijing 100871 (China)

    2014-06-15

    Square Turing patterns are usually unstable in reaction-diffusion systems and are rarely observed in corresponding experiments and simulations. We report here an example of spontaneous formation of square Turing patterns with the Lengyel-Epstein model of two coupled layers. The squares are found to be a result of the resonance between two supercritical Turing modes with an appropriate ratio. Besides, the spatiotemporal resonance of Turing modes resembles to the mode-locking phenomenon. Analysis of the general amplitude equations for square patterns reveals that the fixed point corresponding to square Turing patterns is stationary when the parameters adopt appropriate values.

  7. Spatiotemporal chaos of self-replicating spots in reaction-diffusion systems.

    Science.gov (United States)

    Wang, Hongli; Ouyang, Qi

    2007-11-23

    The statistical properties of self-replicating spots in the reaction-diffusion Gray-Scott model are analyzed. In the chaotic regime of the system, the spots that dominate the spatiotemporal chaos grow and divide in two or decay into the background randomly and continuously. The rates at which the spots are created and decay are observed to be linearly dependent on the number of spots in the system. We derive a probabilistic description of the spot dynamics based on the statistical independence of spots and thus propose a characterization of the spatiotemporal chaos dominated by replicating spots.

  8. Discrete maximum principle for FE solutions of the diffusion-reaction problem on prismatic meshes

    Czech Academy of Sciences Publication Activity Database

    Hannukainen, A.; Korotov, S.; Vejchodský, Tomáš

    2009-01-01

    Roč. 226, č. 2 (2009), s. 275-287 ISSN 0377-0427 R&D Projects: GA AV ČR IAA100760702 Institutional research plan: CEZ:AV0Z10190503 Keywords : diffusion-reaction problem * maximum principle * prismatic finite elements Subject RIV: BA - General Mathematics Impact factor: 1.292, year: 2009

  9. STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies

    Directory of Open Access Journals (Sweden)

    Hepburn Iain

    2012-05-01

    Full Text Available Abstract Background Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins, conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. Results We describe STEPS, a stochastic reaction–diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction–diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. Conclusion STEPS simulates

  10. Multi-layer composite mechanical modeling for the inhomogeneous biofilm mechanical behavior.

    Science.gov (United States)

    Wang, Xiaoling; Han, Jingshi; Li, Kui; Wang, Guoqing; Hao, Mudong

    2016-08-01

    Experiments showed that bacterial biofilms are heterogeneous, for example, the density, the diffusion coefficient, and mechanical properties of the biofilm are different along the biofilm thickness. In this paper, we establish a multi-layer composite model to describe the biofilm mechanical inhomogeneity based on unified multiple-component cellular automaton (UMCCA) model. By using our model, we develop finite element simulation procedure for biofilm tension experiment. The failure limit and biofilm extension displacement obtained from our model agree well with experimental measurements. This method provides an alternative theory to study the mechanical inhomogeneity in biological materials.

  11. Convergence to Equilibrium in Energy-Reaction-Diffusion Systems Using Vector-Valued Functional Inequalities

    Science.gov (United States)

    Mielke, Alexander; Mittnenzweig, Markus

    2018-04-01

    We discuss how the recently developed energy dissipation methods for reaction diffusion systems can be generalized to the non-isothermal case. For this, we use concave entropies in terms of the densities of the species and the internal energy, where the importance is that the equilibrium densities may depend on the internal energy. Using the log-Sobolev estimate and variants for lower-order entropies as well as estimates for the entropy production of the nonlinear reactions, we give two methods to estimate the relative entropy by the total entropy production, namely a somewhat restrictive convexity method, which provides explicit decay rates, and a very general, but weaker compactness method.

  12. Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Windus, Alastair; Jensen, Henrik J [The Institute for Mathematical Sciences, 53 Prince' s Gate, South Kensington, London SW7 2PG (United Kingdom)], E-mail: h.jensen@imperial.ac.uk

    2008-11-15

    We consider a reaction-diffusion model incorporating the reactions A{yields}{phi}, A{yields}2A and 2A{yields}3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. While we comment on this critical behaviour, the main focus of the paper is on the geometry of the population clusters that form. We observe the different cluster structures that arise at criticality for the three different types of critical behaviour and show that there exists a linear relationship for the survival probability against initial cluster size at the tricritical point only.

  13. Modeling and simulation of a controlled steam generator in the context of dynamic reliability using a Stochastic Hybrid Automaton

    International Nuclear Information System (INIS)

    Babykina, Génia; Brînzei, Nicolae; Aubry, Jean-François; Deleuze, Gilles

    2016-01-01

    The paper proposes a modeling framework to support Monte Carlo simulations of the behavior of a complex industrial system. The aim is to analyze the system dependability in the presence of random events, described by any type of probability distributions. Continuous dynamic evolutions of physical parameters are taken into account by a system of differential equations. Dynamic reliability is chosen as theoretical framework. Based on finite state automata theory, the formal model is built by parallel composition of elementary sub-models using a bottom-up approach. Considerations of a stochastic nature lead to a model called the Stochastic Hybrid Automaton. The Scilab/Scicos open source environment is used for implementation. The case study is carried out on an example of a steam generator of a nuclear power plant. The behavior of the system is studied by exploring its trajectories. Possible system trajectories are analyzed both empirically, using the results of Monte Carlo simulations, and analytically, using the formal system model. The obtained results are show to be relevant. The Stochastic Hybrid Automaton appears to be a suitable tool to address the dynamic reliability problem and to model real systems of high complexity; the bottom-up design provides precision and coherency of the system model. - Highlights: • A part of a nuclear power plant is modeled in the context of dynamic reliability. • Stochastic Hybrid Automaton is used as an input model for Monte Carlo simulations. • The model is formally built using a bottom-up approach. • The behavior of the system is analyzed empirically and analytically. • A formally built SHA shows to be a suitable tool to approach dynamic reliability.

  14. Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

    Directory of Open Access Journals (Sweden)

    Roman Cherniha

    2018-04-01

    Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

  15. Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms

    International Nuclear Information System (INIS)

    Sheng Li; Yang Huizhong; Lou Xuyang

    2009-01-01

    This paper presents an exponential synchronization scheme for a class of neural networks with time-varying and distributed delays and reaction-diffusion terms. An adaptive synchronization controller is derived to achieve the exponential synchronization of the drive-response structure of neural networks by using the Lyapunov stability theory. At the same time, the update laws of parameters are proposed to guarantee the synchronization of delayed neural networks with all parameters unknown. It is shown that the approaches developed here extend and improve the ideas presented in recent literatures.

  16. Solid state reaction studies in Fe{sub 3}O{sub 4}–TiO{sub 2} system by diffusion couple method

    Energy Technology Data Exchange (ETDEWEB)

    Ren, Zhongshan [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China); Hu, Xiaojun, E-mail: huxiaojun@ustb.edu.cn [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China); Xue, Xiangxin [School of Materials and Metallurgy, Northeastern University, Shenyang 110006 (China); Chou, Kuochih [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China)

    2013-12-15

    Highlights: •The solid state reactions of Fe2O3-TiO2 system was studied by the diffusion couple method. •Different products were formed by diffusion, and the FeTiO3 was more stable phase. •The inter-diffusion coefficients and diffusion activation energy were estimated. -- Abstract: The solid state reactions in Fe{sub 3}O{sub 4}–TiO{sub 2} system has been studied by diffusion couple experiments at 1323–1473 K, in which the oxygen partial pressure was controlled by the CO–CO{sub 2} gas mixture. The XRD analysis was used to confirm the phases of the inter-compound, and the concentration profiles were determined by electron probe microanalysis (EPMA). Based on the concentration profile of Ti, the inter-diffusion coefficients in Fe{sub 3}O{sub 4} phase, which were both temperature and concentration of Ti ions dependent, were calculated by the modified Boltzmann–Matano method. According to the relation between the thickness of diffusion layer and temperature, the diffusion coefficient of the Fe{sub 3}O{sub 4}–TiO{sub 2} system was obtained. According to the Arrhenius equation, the estimated diffusion activation energy was about 282.1 ± 18.8 kJ mol{sup −1}.

  17. Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

    Science.gov (United States)

    Lu, Benzhuo; Zhou, Y.C.

    2011-01-01

    The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

  18. Pattern formation in three-dimensional reaction-diffusion systems

    Science.gov (United States)

    Callahan, T. K.; Knobloch, E.

    1999-08-01

    Existing group theoretic analysis of pattern formation in three dimensions [T.K. Callahan, E. Knobloch, Symmetry-breaking bifurcations on cubic lattices, Nonlinearity 10 (1997) 1179-1216] is used to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability, the Brusselator model and the Lengyel-Epstein model. Spatially periodic patterns having the periodicity of the simple cubic (SC), face-centered cubic (FCC) or body-centered cubic (BCC) lattices are considered. An efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamellæ, SC, FCC, double-diamond, hexagonal prism, BCC and BCCI states. Both models possess a special wavenumber k* at which the normal form coefficients take on fixed model-independent ratios and both are described by identical bifurcation diagrams. This property is generic for two-species chemical reaction-diffusion models with a single activator and inhibitor.

  19. Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics.

    Science.gov (United States)

    Andres, Jeanne Therese H; Cardoso, Silvana S S

    2012-09-01

    We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

  20. Orientation selection of equiaxed dendritic growth by three-dimensional cellular automaton model

    Energy Technology Data Exchange (ETDEWEB)

    Wei Lei [State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi' an 710072 (China); Lin Xin, E-mail: xlin@nwpu.edu.cn [State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi' an 710072 (China); Wang Meng; Huang Weidong [State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi' an 710072 (China)

    2012-07-01

    A three-dimensional (3-D) adaptive mesh refinement (AMR) cellular automata (CA) model is developed to simulate the equiaxed dendritic growth of pure substance. In order to reduce the mesh induced anisotropy by CA capture rules, a limited neighbor solid fraction (LNSF) method is presented. It is shown that the LNSF method reduced the mesh induced anisotropy based on the simulated morphologies for isotropic interface free energy. An expansion description using two interface free energy anisotropy parameters ({epsilon}{sub 1}, {epsilon}{sub 2}) is used in the present 3-D CA model. It is illustrated by present 3-D CA model that the positive {epsilon}{sub 1} favors the dendritic growth with the Left-Pointing-Angle-Bracket 100 Right-Pointing-Angle-Bracket preferred directions, and negative {epsilon}{sub 2} favors dendritic growth with the Left-Pointing-Angle-Bracket 110 Right-Pointing-Angle-Bracket preferred directions, which has a good agreement with the prediction of the spherical plot of the inverse of the interfacial stiffness. The dendritic growths with the orientation selection between Left-Pointing-Angle-Bracket 100 Right-Pointing-Angle-Bracket and Left-Pointing-Angle-Bracket 110 Right-Pointing-Angle-Bracket are also discussed using the different {epsilon}{sub 1} with {epsilon}{sub 2}=-0.02. It is found that the simulated morphologies by present CA model are as expected from the minimum stiffness criterion.

  1. On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

    Energy Technology Data Exchange (ETDEWEB)

    Plante, Ianik, E-mail: ianik.plante-1@nasa.gov [Wyle Science, Technology & Engineering, 1290 Hercules, Houston, TX 77058 (United States); Devroye, Luc, E-mail: lucdevroye@gmail.com [School of Computer Science, McGill University, 3480 University Street, Montreal H3A 0E9 (Canada)

    2015-09-15

    Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well.

  2. On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

    International Nuclear Information System (INIS)

    Plante, Ianik; Devroye, Luc

    2015-01-01

    Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well

  3. Diffusion-controlled reactions modeling in Geant4-DNA

    Energy Technology Data Exchange (ETDEWEB)

    Karamitros, M., E-mail: matkara@gmail.com [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); CNRS, INCIA, UMR 5287, F-33400 Talence (France); Luan, S. [University of New Mexico, Department of Computer Science, Albuquerque, NM (United States); Bernal, M.A. [Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, SP (Brazil); Allison, J. [Geant4 Associates International Ltd (United Kingdom); Baldacchino, G. [CEA Saclay, IRAMIS, LIDYL, Radiation Physical Chemistry Group, F-91191 Gif sur Yvette Cedex (France); CNRS, UMR3299, SIS2M, F-91191 Gif sur Yvette Cedex (France); Davidkova, M. [Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Francis, Z. [Saint Joseph University, Faculty of Sciences, Department of Physics, Mkalles, Beirut (Lebanon); Friedland, W. [Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Radiation Protection, Ingolstädter Landstr. 1, 85764 Neuherberg (Germany); Ivantchenko, V. [Ecoanalytica, 119899 Moscow (Russian Federation); Geant4 Associates International Ltd (United Kingdom); Ivantchenko, A. [Geant4 Associates International Ltd (United Kingdom); Mantero, A. [SwHaRD s.r.l., via Buccari 9, 16153 Genova (Italy); Nieminem, P.; Santin, G. [ESA-ESTEC, 2200 AG Noordwijk (Netherlands); Tran, H.N. [Division of Nuclear Physics and Faculty of Applied Sciences, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Stepan, V. [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Incerti, S., E-mail: incerti@cenbg.in2p3.fr [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France)

    2014-10-01

    Context Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing all the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k–d tree data structure for quickly locating, for a given molecule, its closest reactants. The

  4. Implicit coupling of turbulent diffusion with chemical reaction mechanisms for prognostic atmospheric dispersion models

    Energy Technology Data Exchange (ETDEWEB)

    Berlowitz, D.R.

    1996-11-01

    In the last few decades the negative impact by humans on the thin atmospheric layer enveloping the earth, the basis for life on this planet, has increased steadily. In order to halt, or at least slow down this development, the knowledge and study of these anthropogenic influence has to be increased and possible remedies have to be suggested. An important tool for these studies are computer models. With their help the atmospheric system can be approximated and the various processes, which have led to the current situation can be quantified. They also serve as an instrument to assess short or medium term strategies to reduce this human impact. However, to assure efficiency as well as accuracy, a careful analysis of the numerous processes involved in the dispersion of pollutants in the atmosphere is called for. This should help to concentrate on the essentials and also prevent excessive usage of sometimes scarce computing resources. The basis of the presented work is the EUMAC Zooming Model (ETM), and particularly the component calculating the dispersion of pollutants in the atmosphere, the model MARS. The model has two main parts: an explicit solver, where the advection and the horizontal diffusion of pollutants are calculated, and an implicit solution mechanism, allowing the joint computation of the change of concentration due to chemical reactions, coupled with the respective influence of the vertical diffusion of the species. The aim of this thesis is to determine particularly the influence of the horizontal components of the turbulent diffusion on the existing implicit solver of the model. Suggestions for a more comprehensive inclusion of the full three dimensional diffusion operator in the implicit solver are made. This is achieved by an appropriate operator splitting. A selection of numerical approaches to tighten the coupling of the diffusion processes with the calculation of the applied chemical reaction mechanisms are examined. (author) figs., tabs., refs.

  5. Design and Realization of an Arabic Morphological Automaton-New Approach for Arabic Morphological Analysis and Generation

    OpenAIRE

    Mourad Gridach; Noureddine Chenfour

    2011-01-01

    Arabic morphological analysis is one of the essential stages in Arabic Natural Language Processing. In this paper we present an approach for Arabic morphological analysis. This approach is based on Arabic morphological automaton (AMAUT). The proposed technique uses a morphological database realized using XMODEL language. Arabic morphology represents a special type of morphological systems because it is based on the concept of scheme to represent Arabic words. We use this concept to develop th...

  6. Boundedness for a system of reaction-diffusion equations with more general Arrhenius term. Pt. 1

    International Nuclear Information System (INIS)

    Okoya, S.S.

    1992-11-01

    In this paper, we consider an extended model of a coupled nonlinear reaction-diffusion equation with Neumann-Neumann boundary conditions. We obtain upper linear growth bound for one of the components. We also find the corresponding bound for the case of Dirichlet-Dirichlet boundary conditions. (author). 12 refs

  7. Brownian motion in a field of force and the diffusion theory of chemical reactions. II

    NARCIS (Netherlands)

    Brinkman, H.C.

    1956-01-01

    H. A. Kramers has studied the rate of chemical reactions in view of the Brownian forces caused by a surrounding medium in temperature equilibrium. In a previous paper 3) the author gave a solution of Kramers' diffusion equation in phase space by systematic development. In this paper the general

  8. Archaic man meets a marvellous automaton: posthumanism, social robots, archetypes.

    Science.gov (United States)

    Jones, Raya

    2017-06-01

    Posthumanism is associated with critical explorations of how new technologies are rewriting our understanding of what it means to be human and how they might alter human existence itself. Intersections with analytical psychology vary depending on which technologies are held in focus. Social robotics promises to populate everyday settings with entities that have populated the imagination for millennia. A legend of A Marvellous Automaton appears as early as 350 B.C. in a book of Taoist teachings, and is joined by ancient and medieval legends of manmade humanoids coming to life, as well as the familiar robots of modern science fiction. However, while the robotics industry seems to be realizing an archetypal fantasy, the technology creates new social realities that generate distinctive issues of potential relevance for the theory and practice of analytical psychology. © 2017, The Society of Analytical Psychology.

  9. Coupled Diffusion and Reaction Processes in Rock Matrices: Impact on Dilute Groundwater Plumes

    Science.gov (United States)

    2015-12-28

    35    3.6.3-Diffusion-Reaction Cell Construction using 40 mL Vials Gas tight extraction cells were designed and constructed to serve as a means to...ground surface GC gas chromatograph HPLC high-performance liquid chromatography ISCO in situ chemical oxidation MNA monitored natural attenuation...fracture-matrix interface. Mazurek et al. (1996) showed that fractures within shales were coated with birnessite and gypsum. Thus, the impacts of

  10. Bifurcation of positive solutions to scalar reaction-diffusion equations with nonlinear boundary condition

    Science.gov (United States)

    Liu, Ping; Shi, Junping

    2018-01-01

    The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.

  11. An Urban Cellular Automata Model for Simulating Dynamic States on a Local Scale

    Directory of Open Access Journals (Sweden)

    Jenni Partanen

    2016-12-01

    Full Text Available In complex systems, flexibility and adaptability to changes are crucial to the systems’ dynamic stability and evolution. Such resilience requires that the system is able to respond to disturbances by self-organizing, which implies a certain level of entropy within the system. Dynamic states (static, cyclical/periodic, complex, and chaotic reflect this generative capacity, and correlate with the level of entropy. For planning complex cities, we need to develop methods to guide such autonomous progress in an optimal manner. A classical apparatus, cellular automaton (CA, provides such a tool. Applications of CA help us to study temporal dynamics in self-organizing urban systems. By exploring the dynamic states of the model’s dynamics resulting from different border conditions it is possible to discover favorable set(s of rules conductive to the self-organizing dynamics and enable the system’s recovery at the time of crises. Level of entropy is a relevant measurement for evaluation of these dynamic states. The 2-D urban cellular automaton model studied here is based on the microeconomic principle that similar urban activities are attracted to each other, especially in certain self-organizing areas, and that the local dynamics of these enclaves affect the dynamics of the urban region by channeling flows of information, goods and people. The results of the modeling experiment indicate that the border conditions have a major impact on the model’s dynamics generating various dynamic states of the system. Most importantly, it seemed that the model could simulate a favorable, complex dynamic state with medium entropy level which may refer to the continuous self-organization of the system. The model provides a tool for exploring and understanding the effects of boundary conditions in the planning process as various scenarios are tested: resulting dynamics of the system can be explored with such “planning rules” prior to decisions, helping to

  12. Multiscale diffusion of a molecular probe in a crowded environment: a concept

    Science.gov (United States)

    Currie, Megan; Thao, Chang; Timerman, Randi; Welty, Robb; Berry, Brenden; Sheets, Erin D.; Heikal, Ahmed A.

    2015-08-01

    Living cells are crowded with macromolecules and organelles. Yet, it is not fully understood how macromolecular crowding affects the myriad of biochemical reactions, transport and the structural stability of biomolecules that are essential to cellular function and survival. These molecular processes, with or without electrostatic interactions, in living cells are therefore expected to be distinct from those carried out in test tube in dilute solutions where excluded volumes are absent. Thus there is an urgent need to understand the macromolecular crowding effects on cellular and molecular biophysics towards quantitative cell biology. In this report, we investigated how biomimetic crowding affects both the rotational and translation diffusion of a small probe (rhodamine green, RhG). For biomimetic crowding agents, we used Ficoll-70 (synthetic polymer), bovine serum albumin and ovalbumin (proteins) at various concentrations in a buffer at room temperature. As a control, we carried out similar measurements on glycerolenriched buffer as an environment with homogeneous viscosity as a function of glycerol concentration. The corresponding bulk viscosity was measured independently to test the validity of the Stokes-Einstein model of a diffusing species undergoing a random walk. For rotational diffusion (ps-ns time scale), we used time-resolved anisotropy measurements to examine potential binding of RhG as a function of the crowding agents (surface structure and size). For translational diffusion (μs-s time scale), we used fluorescence correlation spectroscopy for single-molecule fluctuation analysis. Our results allow us to examine the diffusion model of a molecular probe in crowded environments as a function of concentration, length scale, homogeneous versus heterogeneous viscosity, size and surface structures. These biomimetic crowding studies, using non-invasive fluorescence spectroscopy methods, represent an important step towards understanding cellular biophysics and

  13. A BABCOCK–LEIGHTON SOLAR DYNAMO MODEL WITH MULTI-CELLULAR MERIDIONAL CIRCULATION IN ADVECTION- AND DIFFUSION-DOMINATED REGIMES

    Energy Technology Data Exchange (ETDEWEB)

    Belucz, Bernadett; Forgács-Dajka, Emese [Eötvös University, Department of Astronomy, 1518 Budapest, Pf. 32 (Hungary); Dikpati, Mausumi, E-mail: bbelucz@astro.elte.hu, E-mail: dikpati@ucar.edu [High Altitude Observatory, National Center for Atmospheric Research, 3080 Center Green, Boulder, CO 80307-3000 (United States)

    2015-06-20

    Babcock–Leighton type-solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a single-celled flow pattern. We examine the role of complex multi-cellular circulation patterns in a Babcock–Leighton solar dynamo in advection- and diffusion-dominated regimes. We show from simulations that the presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in the butterfly diagram, whereas the presence of a second cell in depth reverses the tilt of the butterfly wing to an antisolar type. A butterfly diagram constructed from the middle of convection zone yields a solar-like pattern, but this may be difficult to realize in the Sun because of magnetic buoyancy effects. Each of the above cases behaves similarly in higher and lower magnetic diffusivity regimes. However, our dynamo with a meridional circulation containing four cells in latitude behaves distinctly differently in the two regimes, producing solar-like butterfly diagrams with fast cycles in the higher diffusivity regime, and complex branches in butterfly diagrams in the lower diffusivity regime. We also find that dynamo solutions for a four-celled pattern, two in radius and two in latitude, prefer to quickly relax to quadrupolar parity if the bottom flow speed is strong enough, of similar order of magnitude as the surface flow speed.

  14. A BABCOCK–LEIGHTON SOLAR DYNAMO MODEL WITH MULTI-CELLULAR MERIDIONAL CIRCULATION IN ADVECTION- AND DIFFUSION-DOMINATED REGIMES

    International Nuclear Information System (INIS)

    Belucz, Bernadett; Forgács-Dajka, Emese; Dikpati, Mausumi

    2015-01-01

    Babcock–Leighton type-solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a single-celled flow pattern. We examine the role of complex multi-cellular circulation patterns in a Babcock–Leighton solar dynamo in advection- and diffusion-dominated regimes. We show from simulations that the presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in the butterfly diagram, whereas the presence of a second cell in depth reverses the tilt of the butterfly wing to an antisolar type. A butterfly diagram constructed from the middle of convection zone yields a solar-like pattern, but this may be difficult to realize in the Sun because of magnetic buoyancy effects. Each of the above cases behaves similarly in higher and lower magnetic diffusivity regimes. However, our dynamo with a meridional circulation containing four cells in latitude behaves distinctly differently in the two regimes, producing solar-like butterfly diagrams with fast cycles in the higher diffusivity regime, and complex branches in butterfly diagrams in the lower diffusivity regime. We also find that dynamo solutions for a four-celled pattern, two in radius and two in latitude, prefer to quickly relax to quadrupolar parity if the bottom flow speed is strong enough, of similar order of magnitude as the surface flow speed

  15. Ocean acidification affects competition for space: projections of community structure using cellular automata.

    Science.gov (United States)

    McCoy, Sophie J; Allesina, Stefano; Pfister, Catherine A

    2016-03-16

    Historical ecological datasets from a coastal marine community of crustose coralline algae (CCA) enabled the documentation of ecological changes in this community over 30 years in the Northeast Pacific. Data on competitive interactions obtained from field surveys showed concordance between the 1980s and 2013, yet also revealed a reduction in how strongly species interact. Here, we extend these empirical findings with a cellular automaton model to forecast ecological dynamics. Our model suggests the emergence of a new dominant competitor in a global change scenario, with a reduced role of herbivory pressure, or trophic control, in regulating competition among CCA. Ocean acidification, due to its energetic demands, may now instead play this role in mediating competitive interactions and thereby promote species diversity within this guild. © 2016 The Author(s).

  16. Nonlinear waves in reaction-diffusion systems: The effect of transport memory

    International Nuclear Information System (INIS)

    Manne, K. K.; Hurd, A. J.; Kenkre, V. M.

    2000-01-01

    Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity. (c) 2000 The American Physical Society

  17. Nonlinear waves in reaction-diffusion systems: The effect of transport memory

    Science.gov (United States)

    Manne, K. K.; Hurd, A. J.; Kenkre, V. M.

    2000-04-01

    Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.

  18. On the influence of hydronium and hydroxide ion diffusion on the hydrogen and oxygen evolution reactions in aqueous media

    DEFF Research Database (Denmark)

    Wiberg, Gustav Karl Henrik; Arenz, Matthias

    2015-01-01

    We present a study concerning the influence of the diffusion of H+ and OH- ions on the hydrogen and oxygen evolution reactions (HER and OER) in aqueous electrolyte solutions. Using a rotating disk electrode (RDE), it is shown that at certain conditions the observed current, i.e., the reaction rate...

  19. Traveling and Pinned Fronts in Bistable Reaction-Diffusion Systems on Networks

    Science.gov (United States)

    Kouvaris, Nikos E.; Kori, Hiroshi; Mikhailov, Alexander S.

    2012-01-01

    Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erdös-Rényi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erdös-Rényi and scale-free networks, the mean-field theory for stationary patterns is constructed. PMID:23028746

  20. Neural networks, cellular automata, and robust approach applications for vertex localization in the opera target tracker detector

    International Nuclear Information System (INIS)

    Dmitrievskij, S.G.; Gornushkin, Yu.A.; Ososkov, G.A.

    2005-01-01

    A neural-network (NN) approach for neutrino interaction vertex reconstruction in the OPERA experiment with the help of the Target Tracker (TT) detector is described. A feed-forward NN with the standard back propagation option is used. The energy functional minimization of the network is performed by the method of conjugate gradients. Data preprocessing by means of cellular automaton algorithm is performed. The Hough transform is applied for muon track determination and the robust fitting method is used for shower axis reconstruction. A comparison of the proposed approach with earlier studies, based on the use of the neural network package SNNS, shows their similar performance. The further development of the approach is underway

  1. Curved fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R2

    Science.gov (United States)

    Niu, Hong-Tao; Wang, Zhi-Cheng; Bu, Zhen-Hui

    2018-05-01

    In this paper we consider a diffusion system with the Belousov-Zhabotinskii (BZ for short) chemical reaction. Following Brazhnik and Tyson [4] and Pérez-Muñuzuri et al. [45], who predicted V-shaped fronts theoretically and discovered V-shaped fronts by experiments respectively, we give a rigorous mathematical proof of their results. We establish the existence of V-shaped traveling fronts in R2 by constructing a proper supersolution and a subsolution. Furthermore, we establish the stability of the V-shaped front in R2.

  2. Asymptotic analysis of reaction-diffusion-advection problems: Fronts with periodic motion and blow-up

    Science.gov (United States)

    Nefedov, Nikolay

    2017-02-01

    This is an extended variant of the paper presented at MURPHYS-HSFS 2016 conference in Barcelona. We discuss further development of the asymptotic method of differential inequalities to investigate existence and stability of sharp internal layers (fronts) for nonlinear singularly perturbed periodic parabolic problems and initial boundary value problems with blow-up of fronts for reaction-diffusion-advection equations. In particular, we consider periodic solutions with internal layer in the case of balanced reaction. For the initial boundary value problems we prove the existence of fronts and give their asymptotic approximation including the new case of blowing-up fronts. This case we illustrate by the generalised Burgers equation.

  3. Relativistic thermodynamics of irreversible processes I. Heat conduction, diffusion, viscous flow and chemical reactions; formal part

    NARCIS (Netherlands)

    Kluitenberg, G.A.; Groot, S.R. de; Mazur, P.

    1953-01-01

    The relativistic thermodynamics of irreversible processes is developed for an isotropic mixture in which heat conduction, diffusion, viscous flow, chemical reactions and their cross-phenomena may occur. The four-vectors, representing the relative flows of matter, are defined in such a way that, in

  4. Exact quantification of the complexity of spacewise pattern growth in cellular automata

    International Nuclear Information System (INIS)

    Freire, Joana G; Gallas, Jason A C; Brison, Owen J

    2009-01-01

    We analyze the two possible ways of simulating complex systems with cellular automata: by using the familiar timewise updating or by using the complementary spacewise updating. Both updating algorithms operate on identical sets of initial conditions defining the state of the automaton. While timewise growth generally probes just vanishingly small sets of initial conditions producing statistical samples of the asymptotic attractors, spacewise growth operates with much restricted sets which allow one to simulate them all, exhaustively. Our main result is the derivation of an exact analytical formula to quantify precisely one of the two sources of algorithmic complexity of spacewise detection of the complete set of attractors for elementary 1D cellular automata with generic non-periodic architectures of any arbitrary size. The formula gives the total number of initial conditions that need to be investigated to locate rigorously all possible patterns for any given rule. As simple applications, we illustrate how this knowledge may be used (i) to uncover missing patterns in previous classifications in the literature and (ii) to obtain surprisingly novel patterns that are totally unreachable with the time-honored technique of artificially imposing spatially periodic boundary conditions.

  5. Asymptotic behavior of equilibrium states of reaction-diffusion systems with mass conservation

    Science.gov (United States)

    Chern, Jann-Long; Morita, Yoshihisa; Shieh, Tien-Tsan

    2018-01-01

    We deal with a stationary problem of a reaction-diffusion system with a conservation law under the Neumann boundary condition. It is shown that the stationary problem turns to be the Euler-Lagrange equation of an energy functional with a mass constraint. When the domain is the finite interval (0 , 1), we investigate the asymptotic profile of a strictly monotone minimizer of the energy as d, the ratio of the diffusion coefficient of the system, tends to zero. In view of a logarithmic function in the leading term of the potential, we get to a scaling parameter κ satisfying the relation ε : =√{ d } =√{ log ⁡ κ } /κ2. The main result shows that a sequence of minimizers converges to a Dirac mass multiplied by the total mass and that by a scaling with κ the asymptotic profile exhibits a parabola in the nonvanishing region. We also prove the existence of an unstable monotone solution when the mass is small.

  6. Passivity analysis for uncertain BAM neural networks with time delays and reaction-diffusions

    Science.gov (United States)

    Zhou, Jianping; Xu, Shengyuan; Shen, Hao; Zhang, Baoyong

    2013-08-01

    This article deals with the problem of passivity analysis for delayed reaction-diffusion bidirectional associative memory (BAM) neural networks with weight uncertainties. By using a new integral inequality, we first present a passivity condition for the nominal networks, and then extend the result to the case with linear fractional weight uncertainties. The proposed conditions are expressed in terms of linear matrix inequalities, and thus can be checked easily. Examples are provided to demonstrate the effectiveness of the proposed results.

  7. Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

    Energy Technology Data Exchange (ETDEWEB)

    Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan); Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610 (Belgium); Chen, W. [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan)

    2016-08-07

    Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realistic biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.

  8. Resonant elastic scattering, inelastic scattering and astrophysical reactions; Diffusion elastique resonante, diffusion inelastique et reactions astrophysiques

    Energy Technology Data Exchange (ETDEWEB)

    De Oliveira Santos, F. [Grand Accelerateur National d' Ions Lourds, UMR 6415, 14 - Caen (France)

    2007-07-01

    Nuclear reactions can occur at low kinetic energy. Low-energy reactions are characterized by a strong dependence on the structure of the compound nucleus. It turns out that it is possible to study the nuclear structure by measuring these reactions. In this course, three types of reactions are treated: Resonant Elastic Scattering (such as N{sup 14}(p,p)N{sup 14}), Inelastic Scattering (such as N{sup 14}(p,p')N{sup 14*}) and Astrophysical reactions (such as N{sup 14}(p,{gamma})O{sup 15}). (author)

  9. Observations of cellular transformation products in nickel-base superalloys

    International Nuclear Information System (INIS)

    Barlow, C.Y.; Ralph, B.

    1979-01-01

    Transmission electron microscopy has been used to identify the products in cellularly transformed regions of alloys based on the Nimonic 80 A composition. The commercial alloy is shown to undergo a small degree of cellular transformation even after conventional heat treatments, while recrystallization is found to increase the incidence of this reaction type. Low carbon versions of this alloy demonstrate cellular precipitation over a wider range of heat treatments. It is shown that the cellular reaction may take place in these alloys under a variety of different conditions and with a range of driving forces. Reasons for this unexpected behaviour are offeredm as is a suggestion as to why the cellular reaction occurs on a local scale. (author)

  10. Modelling of Eutectic Saturation Influence on Microstructure in Thin Wall Ductile Iron Casting Using Cellular Automata

    Directory of Open Access Journals (Sweden)

    Burbelko A.A.

    2012-12-01

    Full Text Available The mathematical model of the globular eutectic solidification in 2D was designed. Proposed model is based on the Cellular Automaton Finite Differences (CA-FD calculation method. Model has been used for studies of the primary austenite and of globular eutectic grains growth during the ductile iron solidification in the thin wall casting. Model takes into account, among other things, non-uniform temperature distribution in the casting wall cross-section, kinetics of the austenite and graphite grains nucleation, and non-equilibrium nature of the interphase boundary migration. Calculation of eutectic saturation influence (Sc = 0.9 - 1.1 on microstructure (austenite and graphite fraction, density of austenite and graphite grains and temperature curves in 2 mm wall ductile iron casting has been done.

  11. A DNA Logic Gate Automaton for Detection of Rabies and Other Lyssaviruses.

    Science.gov (United States)

    Vijayakumar, Pavithra; Macdonald, Joanne

    2017-07-05

    Immediate activation of biosensors is not always desirable, particularly if activation is due to non-specific interactions. Here we demonstrate the use of deoxyribozyme-based logic gate networks arranged into visual displays to precisely control activation of biosensors, and demonstrate a prototype molecular automaton able to discriminate between seven different genotypes of Lyssaviruses, including Rabies virus. The device uses novel mixed-base logic gates to enable detection of the large diversity of Lyssavirus sequence populations, while an ANDNOT logic gate prevents non-specific activation across genotypes. The resultant device provides a user-friendly digital-like, but molecule-powered, dot-matrix text output for unequivocal results read-out that is highly relevant for point of care applications. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

  12. Global exponential stability for reaction-diffusion recurrent neural networks with multiple time varying delays

    International Nuclear Information System (INIS)

    Lou, X.; Cui, B.

    2008-01-01

    In this paper we consider the problem of exponential stability for recurrent neural networks with multiple time varying delays and reaction-diffusion terms. The activation functions are supposed to be bounded and globally Lipschitz continuous. By means of Lyapunov functional, sufficient conditions are derived, which guarantee global exponential stability of the delayed neural network. Finally, a numerical example is given to show the correctness of our analysis. (author)

  13. A reaction-diffusion model for market fluctuations - A relation between price change and traded volumes

    Science.gov (United States)

    Yuvan, Steven; Bier, Martin

    2018-02-01

    Two decades ago Bak et al. (1997) [3] proposed a reaction-diffusion model to describe market fluctuations. In the model buyers and sellers diffuse from opposite ends of a 1D interval that represents a price range. Trades occur when buyers and sellers meet. We show analytically and numerically that the model well reproduces the square-root relation between traded volumes and price changes that is observed in real-life markets. The result is remarkable as this relation has commonly been explained in terms of more elaborate trader strategies. We furthermore explain why the square-root relation is robust under model modifications and we show how real-life bond market data exhibit the square-root relation.

  14. A Local Land Use Competition Cellular Automata Model and Its Application

    Directory of Open Access Journals (Sweden)

    Jun Yang

    2016-06-01

    Full Text Available Cellular automaton (CA is an important method in land use and cover change studies, however, the majority of research focuses on the discovery of macroscopic factors affecting LUCC, which results in ignoring the local effects within the neighborhoods. This paper introduces a Local Land Use Competition Cellular Automata (LLUC-CA model, based on local land use competition, land suitability evaluation, demand analysis of the different land use types, and multi-target land use competition allocation algorithm to simulate land use change at a micro level. The model is applied to simulate land use changes at Jinshitan National Tourist Holiday Resort from 1988 to 2012. The results show that the simulation accuracies were 64.46%, 77.21%, 85.30% and 99.14% for the agricultural land, construction land, forestland and water, respectively. In addition, comparing the simulation results of the LLUC-CA and CA-Markov model with the real land use data, their overall spatial accuracies were found to be 88.74% and 86.82%, respectively. In conclusion, the results from this study indicated that the model was an acceptable method for the simulation of large-scale land use changes, and the approach used here is applicable to analyzing the land use change driven forces and assist in decision-making.

  15. Stochastic flows, reaction-diffusion processes, and morphogenesis

    International Nuclear Information System (INIS)

    Kozak, J.J.; Hatlee, M.D.; Musho, M.K.; Politowicz, P.A.; Walsh, C.A.

    1983-01-01

    Recently, an exact procedure has been introduced [C. A. Walsh and J. J. Kozak, Phys. Rev. Lett.. 47: 1500 (1981)] for calculating the expected walk length for a walker undergoing random displacements on a finite or infinite (periodic) d-dimensional lattice with traps (reactive sites). The method (which is based on a classification of the symmetry of the sites surrounding the central deep trap and a coding of the fate of the random walker as it encounters a site of given symmetry) is applied here to several problems in lattice statistics for each of which exact results are presented. First, we assess the importance of lattice geometry in influencing the efficiency of reaction-diffusion processs in simple and multiple trap systems by reporting values of for square (cubic) versus hexagonal lattices in d = 2,3. We then show how the method may be applied to variable-step (distance-dependent) walks for a single walker on a given lattice and also demonstrate the calculation of the expected walk length for the case of multiple walkers. Finally, we make contact with recent discussions of ''mixing'' by showing that the degree of chaos associated with flows in certain lattice-systems can be calibrated by monitoring the lattice walks induced by the Poincare map of a certain parabolic function

  16. Delay-induced Turing-like waves for one-species reaction-diffusion model on a network

    Science.gov (United States)

    Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio

    2015-09-01

    A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.

  17. Conway's Game of Life is a near-critical metastable state in the multiverse of cellular automata.

    Science.gov (United States)

    Reia, Sandro M; Kinouchi, Osame

    2014-05-01

    Conway's cellular automaton Game of Life has been conjectured to be a critical (or quasicritical) dynamical system. This criticality is generally seen as a continuous order-disorder transition in cellular automata (CA) rule space. Life's mean-field return map predicts an absorbing vacuum phase (ρ = 0) and an active phase density, with ρ = 0.37, which contrasts with Life's absorbing states in a square lattice, which have a stationary density of ρ(2D) ≈ 0.03. Here, we study and classify mean-field maps for 6144 outer-totalistic CA and compare them with the corresponding behavior found in the square lattice. We show that the single-site mean-field approach gives qualitative (and even quantitative) predictions for most of them. The transition region in rule space seems to correspond to a nonequilibrium discontinuous absorbing phase transition instead of a continuous order-disorder one. We claim that Life is a quasicritical nucleation process where vacuum phase domains invade the alive phase. Therefore, Life is not at the "border of chaos," but thrives on the "border of extinction."

  18. Incorporating drug delivery into an imaging-driven, mechanics-coupled reaction diffusion model for predicting the response of breast cancer to neoadjuvant chemotherapy: theory and preliminary clinical results

    Science.gov (United States)

    Jarrett, Angela M.; Hormuth, David A.; Barnes, Stephanie L.; Feng, Xinzeng; Huang, Wei; Yankeelov, Thomas E.

    2018-05-01

    Clinical methods for assessing tumor response to therapy are largely rudimentary, monitoring only temporal changes in tumor size. Our goal is to predict the response of breast tumors to therapy using a mathematical model that utilizes magnetic resonance imaging (MRI) data obtained non-invasively from individual patients. We extended a previously established, mechanically coupled, reaction-diffusion model for predicting tumor response initialized with patient-specific diffusion weighted MRI (DW-MRI) data by including the effects of chemotherapy drug delivery, which is estimated using dynamic contrast-enhanced (DCE-) MRI data. The extended, drug incorporated, model is initialized using patient-specific DW-MRI and DCE-MRI data. Data sets from five breast cancer patients were used—obtained before, after one cycle, and at mid-point of neoadjuvant chemotherapy. The DCE-MRI data was used to estimate spatiotemporal variations in tumor perfusion with the extended Kety–Tofts model. The physiological parameters derived from DCE-MRI were used to model changes in delivery of therapy drugs within the tumor for incorporation in the extended model. We simulated the original model and the extended model in both 2D and 3D and compare the results for this five-patient cohort. Preliminary results show reductions in the error of model predicted tumor cellularity and size compared to the experimentally-measured results for the third MRI scan when therapy was incorporated. Comparing the two models for agreement between the predicted total cellularity and the calculated total cellularity (from the DW-MRI data) reveals an increased concordance correlation coefficient from 0.81 to 0.98 for the 2D analysis and 0.85 to 0.99 for the 3D analysis (p  <  0.01 for each) when the extended model was used in place of the original model. This study demonstrates the plausibility of using DCE-MRI data as a means to estimate drug delivery on a patient-specific basis in predictive models and

  19. Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

    Science.gov (United States)

    Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian

    2018-03-01

    The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.

  20. Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD

    International Nuclear Information System (INIS)

    Armesto, Nestor; Bondarenko, Sergey; Quiroga-Arias, Paloma; Milhano, Jose Guilherme

    2008-01-01

    We examine numerically different zero-dimensional reaction-diffusion processes as candidate toy models for high-energy QCD evolution. Of the models examined-Reggeon Field Theory, Directed Percolation and Reversible Processes-only the latter shows the behaviour commonly expected, namely an increase of the scattering amplitude with increasing rapidity. Further, we find that increasing recombination terms, quantum loops and the heuristic inclusion of a running of the couplings, generically slow down the evolution.

  1. Asymptotic properties of blow-up solutions in reaction-diffusion equations with nonlocal boundary flux

    Science.gov (United States)

    Liu, Bingchen; Dong, Mengzhen; Li, Fengjie

    2018-04-01

    This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.

  2. Hybrid cellular automaton modeling of nutrient modulated cell growth in tissue engineering constructs.

    Science.gov (United States)

    Chung, C A; Lin, Tze-Hung; Chen, Shih-Di; Huang, Hsing-I

    2010-01-21

    Mathematic models help interpret experimental results and accelerate tissue engineering developments. We develop in this paper a hybrid cellular automata model that combines the differential nutrient transport equation to investigate the nutrient limited cell construct development for cartilage tissue engineering. Individual cell behaviors of migration, contact inhibition and cell collision, coupled with the cell proliferation regulated by oxygen concentration were carefully studied. Simplified two-dimensional simulations were performed. Using this model, we investigated the influence of cell migration speed on the overall cell growth within in vitro cell scaffolds. It was found that intense cell motility can enhance initial cell growth rates. However, since cell growth is also significantly modulated by the nutrient contents, intense cell motility with conventional uniform cell seeding method may lead to declined cell growth in the final time because concentrated cell population has been growing around the scaffold periphery to block the nutrient transport from outside culture media. Therefore, homogeneous cell seeding may not be a good way of gaining large and uniform cell densities for the final results. We then compared cell growth in scaffolds with various seeding modes, and proposed a seeding mode with cells initially residing in the middle area of the scaffold that may efficiently reduce the nutrient blockage and result in a better cell amount and uniform cell distribution for tissue engineering construct developments.

  3. Neuro-Fuzzy Prediction of Cooperation Interaction Profile of Flexible Road Train Based on Hybrid Automaton Modeling

    Directory of Open Access Journals (Sweden)

    Banjanovic-Mehmedovic Lejla

    2016-01-01

    Full Text Available Accurate prediction of traffic information is important in many applications in relation to Intelligent Transport systems (ITS, since it reduces the uncertainty of future traffic states and improves traffic mobility. There is a lot of research done in the field of traffic information predictions such as speed, flow and travel time. The most important research was done in the domain of cooperative intelligent transport system (C-ITS. The goal of this paper is to introduce the novel cooperation behaviour profile prediction through the example of flexible Road Trains useful road cooperation parameter, which contributes to the improvement of traffic mobility in Intelligent Transportation Systems. This paper presents an approach towards the control and cooperation behaviour modelling of vehicles in the flexible Road Train based on hybrid automaton and neuro-fuzzy (ANFIS prediction of cooperation profile of the flexible Road Train. Hybrid automaton takes into account complex dynamics of each vehicle as well as discrete cooperation approach. The ANFIS is a particular class of the ANN family with attractive estimation and learning potentials. In order to provide statistical analysis, RMSE (root mean square error, coefficient of determination (R2 and Pearson coefficient (r, were utilized. The study results suggest that ANFIS would be an efficient soft computing methodology, which could offer precise predictions of cooperative interactions between vehicles in Road Train, which is useful for prediction mobility in Intelligent Transport systems.

  4. Asymptotic stability of a coupled advection-diffusion-reaction system arising in bioreactor processes

    Directory of Open Access Journals (Sweden)

    Maria Crespo

    2017-08-01

    Full Text Available In this work, we present an asymptotic analysis of a coupled system of two advection-diffusion-reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacteria, called biomass, and a diluted organic contaminant (e.g., nitrates, called substrate, in a continuous flow bioreactor. This system exhibits, under suitable conditions, two stable equilibrium states: one steady state in which the biomass becomes extinct and no reaction is produced, called washout, and another steady state, which corresponds to the partial elimination of the substrate. We use the linearization method to give sufficient conditions for the linear asymptotic stability of the two stable equilibrium configurations. Finally, we compare our asymptotic analysis with the usual asymptotic analysis associated to the continuous bioreactor when it is modeled with ordinary differential equations.

  5. 4D Biofabrication of Branching Multicellular Structures: A Morphogenesis Simulation Based on Turing’s Reaction-Diffusion Dynamics

    Science.gov (United States)

    Zhu, Xiaolu; Yang, Hao

    2017-12-01

    The recently emerged four-dimensional (4D) biofabrication technique aims to create dynamic three-dimensional (3D) biological structures that can transform their shapes or functionalities with time when an external stimulus is imposed or when cell postprinting self-assembly occurs. The evolution of 3D pattern of branching geometry via self-assembly of cells is critical for 4D biofabrication of artificial organs or tissues with branched geometry. However, it is still unclear that how the formation and evolution of these branching pattern are biologically encoded. We study the 4D fabrication of lung branching structures utilizing a simulation model on the reaction-diffusion mechanism, which is established using partial differential equations of four variables, describing the reaction and diffusion process of morphogens with time during the development process of lung branching. The simulation results present the forming process of 3D branching pattern, and also interpret the behaviors of side branching and tip splitting as the stalk growing, through 3D visualization of numerical simulation.

  6. Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

    Science.gov (United States)

    Stamova, Ivanka; Stamov, Gani

    2017-12-01

    In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.

  7. Traveling wave solutions of a biological reaction-convection-diffusion equation model by using $(G'/G$ expansion method

    Directory of Open Access Journals (Sweden)

    Shahnam Javadi

    2013-07-01

    Full Text Available In this paper, the $(G'/G$-expansion method is applied to solve a biological reaction-convection-diffusion model arising in mathematical biology. Exact traveling wave solutions are obtained by this method. This scheme can be applied to a wide class of nonlinear partial differential equations.

  8. Simulating flaring events in complex active regions driven by observed magnetograms

    Science.gov (United States)

    Dimitropoulou, M.; Isliker, H.; Vlahos, L.; Georgoulis, M. K.

    2011-05-01

    Context. We interpret solar flares as events originating in active regions that have reached the self organized critical state, by using a refined cellular automaton model with initial conditions derived from observations. Aims: We investigate whether the system, with its imposed physical elements, reaches a self organized critical state and whether well-known statistical properties of flares, such as scaling laws observed in the distribution functions of characteristic parameters, are reproduced after this state has been reached. Methods: To investigate whether the distribution functions of total energy, peak energy and event duration follow the expected scaling laws, we first applied a nonlinear force-free extrapolation that reconstructs the three-dimensional magnetic fields from two-dimensional vector magnetograms. We then locate magnetic discontinuities exceeding a threshold in the Laplacian of the magnetic field. These discontinuities are relaxed in local diffusion events, implemented in the form of cellular automaton evolution rules. Subsequent loading and relaxation steps lead the system to self organized criticality, after which the statistical properties of the simulated events are examined. Physical requirements, such as the divergence-free condition for the magnetic field vector, are approximately imposed on all elements of the model. Results: Our results show that self organized criticality is indeed reached when applying specific loading and relaxation rules. Power-law indices obtained from the distribution functions of the modeled flaring events are in good agreement with observations. Single power laws (peak and total flare energy) are obtained, as are power laws with exponential cutoff and double power laws (flare duration). The results are also compared with observational X-ray data from the GOES satellite for our active-region sample. Conclusions: We conclude that well-known statistical properties of flares are reproduced after the system has

  9. Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

    Science.gov (United States)

    Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

    2018-01-01

    In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

  10. Localization of (photorespiration and CO2 re-assimilation in tomato leaves investigated with a reaction-diffusion model.

    Directory of Open Access Journals (Sweden)

    Herman N C Berghuijs

    Full Text Available The rate of photosynthesis depends on the CO2 partial pressure near Rubisco, Cc, which is commonly calculated by models using the overall mesophyll resistance. Such models do not explain the difference between the CO2 level in the intercellular air space and Cc mechanistically. This problem can be overcome by reaction-diffusion models for CO2 transport, production and fixation in leaves. However, most reaction-diffusion models are complex and unattractive for procedures that require a large number of runs, like parameter optimisation. This study provides a simpler reaction-diffusion model. It is parameterized by both leaf physiological and leaf anatomical data. The anatomical data consisted of the thickness of the cell wall, cytosol and stroma, and the area ratios of mesophyll exposed to the intercellular air space to leaf surfaces and exposed chloroplast to exposed mesophyll surfaces. The model was used directly to estimate photosynthetic parameters from a subset of the measured light and CO2 response curves; the remaining data were used for validation. The model predicted light and CO2 response curves reasonably well for 15 days old tomato (cv. Admiro leaves, if (photorespiratory CO2 release was assumed to take place in the inner cytosol or in the gaps between the chloroplasts. The model was also used to calculate the fraction of CO2 produced by (photorespiration that is re-assimilated in the stroma, and this fraction ranged from 56 to 76%. In future research, the model should be further validated to better understand how the re-assimilation of (photorespired CO2 is affected by environmental conditions and physiological parameters.

  11. Modelling for near-surface interaction of lithium ceramics and sweep-gas by use of cellular automation

    International Nuclear Information System (INIS)

    Shimura, K.; Terai, T.; Yamawaki, M.; Yamaguchi, K.

    2003-01-01

    Tritium release from the lithium ceramics as a fusion reactor breeder material is strongly affected by the composition of the sweep-gas as result of its influences with the material's surface. The typical surface processes which play important roles are adsorption, desorption and interaction between vacancy site and the constituents of the sweep-gas. Among a large number of studies and models, yet it seems to be difficult to model the overall behaviour of those processes due to its complex time-transient nature. In the present work the coarse grained atomic simulation based on the Cellular Automaton (CA) is used to model the dynamics of near-surface interaction between Li 2 O surface and sweep-gas that is consisting of a noble gas, hydrogen gas and water vapour. (author)

  12. Diffusion-limited reactions of hard-core particles in one dimension

    Science.gov (United States)

    Bares, P.-A.; Mobilia, M.

    1999-02-01

    We investigate three different methods to tackle the problem of diffusion-limited reactions (annihilation) of hard-core classical particles in one dimension. We first extend an approach devised by Lushnikov [Sov. Phys. JETP 64, 811 (1986)] and calculate for a single species the asymptotic long-time and/or large-distance behavior of the two-point correlation function. Based on a work by Grynberg and Stinchcombe [Phys. Rev. E 50, 957 (1994); Phys. Rev. Lett. 74, 1242 (1995); 76, 851 (1996)], which was developed to treat stochastic adsorption-desorption models, we provide in a second step the exact two-point (one- and two-time) correlation functions of Lushnikov's model. We then propose a formulation of the problem in terms of path integrals for pseudo- fermions. This formalism can be used to advantage in the multispecies case, especially when applying perturbative renormalization group techniques.

  13. The cellular automaton interpretation of quantum mechanics

    CERN Document Server

    't Hooft, Gerard

    2016-01-01

    This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The book presents examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of...

  14. Cellular automaton simulation of microstructure evolution during ...

    Indian Academy of Sciences (India)

    Unknown

    different composition and austenite grain size. Using the ..... Figure 1. Microstructures of 0⋅28% C steel heat treated samples: a. cooling rate 1⋅75°C/S and equivalent grain diameter .... qualitative predictions point to the essential soundness.

  15. A variational approach to bifurcation points of a reaction-diffusion system with obstacles and neumann boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Eisner, Jan; Kučera, Milan; Väth, Martin

    2016-01-01

    Roč. 61, č. 1 (2016), s. 1-25 ISSN 0862-7940 R&D Projects: GA ČR GA13-12580S Institutional support: RVO:67985904 ; RVO:67985840 Keywords : reaction-diffusion system * unlateral condition * variational inequality Subject RIV: EG - Zoology; BA - General Mathematics (MU-W) Impact factor: 0.618, year: 2016

  16. A Reaction-Diffusion Model for Synapse Growth and Long-Term Memory

    Science.gov (United States)

    Liu, Kang; Lisman, John; Hagan, Michael

    Memory storage involves strengthening of synaptic transmission known as long-term potentiation (LTP). The late phase of LTP is associated with structural processes that enlarge the synapse. Yet, synapses must be stable, despite continual subunit turnover, over the lifetime of an encoded memory. These considerations suggest that synapses are variable-size stable structure (VSSS), meaning they can switch between multiple metastable structures with different sizes. The mechanisms underlying VSSS are poorly understood. While experiments and theory have suggested that the interplay between diffusion and receptor-scaffold interactions can lead to a preferred stable size for synaptic domains, such a mechanism cannot explain how synapses adopt widely different sizes. Here we develop a minimal reaction-diffusion model of VSSS for synapse growth, incorporating the recent observation from super-resolution microscopy that neural activity can build compositional heterogeneities within synaptic domains. We find that introducing such heterogeneities can change the stable domain size in a controlled manner. We discuss a potential connection between this model and experimental data on synapse sizes, and how it provides a possible mechanism to structurally encode graded long-term memory. We acknowledge the support from NSF INSPIRE Award number IOS-1526941 (KL, MFH, JL) and the Brandeis Center for Bioinspired Soft Materials, an NSF MRSEC, DMR- 1420382 (MFH).

  17. Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis

    KAUST Repository

    Ibragimov, Akif

    2010-01-01

    This paper presents a linear, asymptotic stability analysis for a reaction-diffusionconvection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross, atherogenesis is viewed as an inflammatory spiral with a positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. The inflammatory spiral is initiated as an instability from a healthy state which is defined to be an equilibrium state devoid of certain key inflammatory markers. Disease initiation is studied through a linear, asymptotic stability analysis of a healthy equilibrium state. Various theorems are proved, giving conditions on system parameters guaranteeing stability of the health state, and a general framework is developed for constructing perturbations from a healthy state that exhibit blow-up, which are interpreted as corresponding to disease initiation. The analysis reveals key features that arterial geometry, antioxidant levels, and the source of inflammatory components (through coupled third-kind boundary conditions or through body sources) play in disease initiation. © 2010 Society for Industrial and Applied Mathematics.

  18. Solid state diffusion and reaction in ZnO/SiO{sub 2} in thin films

    Energy Technology Data Exchange (ETDEWEB)

    Jakob, A; Stucki, S; Schnyder, B; Koetz, R [Paul Scherrer Inst. (PSI), Villigen (Switzerland)

    1997-06-01

    Detoxification of fly ash from waste incineration by evaporating harmful heavy metals is limited by the formation of stable heavy metal-matrix compounds. To study the rate of these heavy metal-matrix reactions, experiments were performed with the diffusion couple ZnO (heavy metal)-SiO{sub 2} (matrix). The atomic concentration profiles after different annealing treatments were analysed by X-ray photoelectron spectroscopy (XPS). (author) 3 figs., 4 refs.

  19. A cardiac electrical activity model based on a cellular automata system in comparison with neural network model.

    Science.gov (United States)

    Khan, Muhammad Sadiq Ali; Yousuf, Sidrah

    2016-03-01

    Cardiac Electrical Activity is commonly distributed into three dimensions of Cardiac Tissue (Myocardium) and evolves with duration of time. The indicator of heart diseases can occur randomly at any time of a day. Heart rate, conduction and each electrical activity during cardiac cycle should be monitor non-invasively for the assessment of "Action Potential" (regular) and "Arrhythmia" (irregular) rhythms. Many heart diseases can easily be examined through Automata model like Cellular Automata concepts. This paper deals with the different states of cardiac rhythms using cellular automata with the comparison of neural network also provides fast and highly effective stimulation for the contraction of cardiac muscles on the Atria in the result of genesis of electrical spark or wave. The specific formulated model named as "States of automaton Proposed Model for CEA (Cardiac Electrical Activity)" by using Cellular Automata Methodology is commonly shows the three states of cardiac tissues conduction phenomena (i) Resting (Relax and Excitable state), (ii) ARP (Excited but Absolutely refractory Phase i.e. Excited but not able to excite neighboring cells) (iii) RRP (Excited but Relatively Refractory Phase i.e. Excited and able to excite neighboring cells). The result indicates most efficient modeling with few burden of computation and it is Action Potential during the pumping of blood in cardiac cycle.

  20. Two-material optimization of plate armour for blast mitigation using hybrid cellular automata

    Science.gov (United States)

    Goetz, J.; Tan, H.; Renaud, J.; Tovar, A.

    2012-08-01

    With the increased use of improvised explosive devices in regions at war, the threat to military and civilian life has risen. Cabin penetration and gross acceleration are the primary threats in an explosive event. Cabin penetration crushes occupants, damaging the lower body. Acceleration causes death at high magnitudes. This investigation develops a process of designing armour that simultaneously mitigates cabin penetration and acceleration. The hybrid cellular automaton (HCA) method of topology optimization has proven efficient and robust in problems involving large, plastic deformations such as crash impact. Here HCA is extended to the design of armour under blast loading. The ability to distribute two metallic phases, as opposed to one material and void, is also added. The blast wave energy transforms on impact into internal energy (IE) inside the solid medium. Maximum attenuation occurs with maximized IE. The resulting structures show HCA's potential for designing blast mitigating armour structures.